Triggered molecular geometry based bioimaging probes

ABSTRACT

The present embodiments relate to engineering imaging probes based on “triggered molecular geometry.” Upon detection of a molecular signal, nucleic acid hairpin monomers assemble an imageable molecular shape with prescribed geometry. In some embodiments the prescribed shape can be imaged directly. In some embodiments, the prescribed shape can serve as a spatial organizer or amplification scheme for other imaging entities, such as fluorophore and fluorescent proteins.

REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional Application No. 61/366,074, filed Jul. 20, 2010, which is incorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED R&D

This invention was made with government support under grant #5P50HG004071 awarded by the NIH. The government has certain rights in the invention.

SEQUENCE LISTING IN ELECTRONIC FORMAT

The present application is being filed along with a Sequence Listing in electronic format. The Sequence Listing is provided as a file entitled SEQLIST_CALTE071A.txt, created on Jul. 19, 2011, which is 24,740 bytes in size. The information in the electronic format of the Sequence Listing is incorporated herein by reference in its entirety.

BACKGROUND

1. Field

The present invention relates generally to imaging probes based on triggered molecular geometry.

2. Background

Microscopic imaging is a powerful tool for studying biologic systems. At the heart of microscopy is the imaging probe, which transduces invisible biological information, such as an mRNA sequence to an imageable signal. At present, imaging probes are mostly constructed by engineering the optical, chemical, and physical properties of imaging probes to produce tailored optical properties. Commonly used imaging probes such as fluorescent proteins (e.g. green fluorescent protein (GFP) and red fluorescent protein (RFP)) and small-molecule dyes (e.g. DAPI, fluorescein, and rhodamine) rely on fluorescence to transduce biological information into an imageable signal. A key challenge in fluorescence bioimaging is the detection many distinct targets simultaneously. Using current practices, between 3 and 6 fluorescent species can be spectrally resolved, setting an upper bound to the number of probes that can be simultaneously employed. This limitation presents a significant technical hurdle in the study of gene expression using single cell fluorescence microscopy, where the number of spectrally distinguishable fluorophores sets an upper bound for the distinct mRNA species that can be simultaneously monitored in a cell.

Another imaging technique, cryo-electron tomography, also known as electron cryotomography, is a type of electron cryomicroscopy that can be used to obtain structural details of complex cellular organizations at subnanometer resolutions. Electron cryotomography uses tomography to obtain a 3D reconstruction of a sample from tilted 2D images at cryogenic temperatures. This enables the study of organelles and the supramolecular architecture of cells in a native state. A long standing challenge in electron cryotomography, however, is the lack of visual markers that can be used to uniquely identify the target proteins.

SUMMARY

In some embodiments, there is a need for imaging probes that possess imageable characteristics that are uniquely identifiable.

In some embodiments, the present teachings provide methods and products for biomolecular self-assembly pathways. In some embodiments, these methods and products can be in initiating and/or carrying out dynamic functions. In some embodiments, methods and compositions disclosed herein are beneficial for providing, for example without limitation, bio-markers and smart therapeutics that can detect a disease marker and then activate a therapeutic biological pathway.

In some embodiments, a hairpin monomer for performing a dynamic function is provided. The hairpin monomer comprises a first domain comprising a first toehold and a first propagation region, wherein the first toehold is exposed such that it is available to hybridize to a portion of a first nucleic acid sequence complementary to the first domain, and wherein the first toehold is located at an end of the monomer; and a second domain comprising a second toehold, wherein the second toehold is hybridized to a portion of the first propagation region.

In some embodiments the first nucleic acid sequence can be complementary to the first domain comprises a portion of an initiator molecule. In some embodiments the second toehold is configured to become available to hybridize to a second nucleic acid sequence of a second monomer if the first domain hybridizes to said initiator molecule.

In some embodiments the second domain further comprises a second propagation region, wherein said second propagation region is complementary to a portion of a second monomer. In some embodiments the said second toehold is configured to become available to initiate hybridization of said second propagation region to said portion of said second monomer if the first domain hybridizes to said first nucleic acid sequence complementary to said first domain. In some embodiments the second propagation region comprises a portion of a single stranded hairpin loop. The second propagation region can be configured not to initiate hybridization to said second monomer if the first domain hybridizes to the first nucleic acid sequence complementary to said first domain.

In some embodiments, the first domain is an input domain and the second domain is an output domain. In some embodiments, a portion of the first propagation region and the second toehold comprise a portion of a duplex stem.

In some embodiments, the hairpin monomer further comprises a third domain comprising a third toehold and a third propagation region, wherein the third toehold is hybridized to a portion of the first propagation region, and the third propagation region is single stranded.

In some embodiments the first toehold is single stranded. In some embodiments the first domain and second domain are concatenated in the monomer. In some embodiments the first domain and second domain are distinct and do not overlap.

In some embodiments, a method for initiating a dynamic function is provided. The method comprises: providing a first hairpin monomer comprising a first domain comprising a first toehold and a first propagation region, wherein the first toehold is exposed such that it is available to hybridize to a portion of a first nucleic acid sequence complementary to the first domain, and wherein the first toehold is located at an end of the monomer; and a second domain comprising a second toehold and a second propagation region, wherein the second toehold is hybridized to a portion of the first propagation region; and providing a second hairpin monomer. In some embodiments, the second hairpin monomer can comprise an input domain comprising a third toehold and a third propagation region, wherein the third toehold is exposed and complementary to the second toehold of the first hairpin monomer; and an output domain.

In some embodiments, the method further comprises providing a third hairpin monomer. In some embodiments, the method further comprises providing a fourth hairpin monomer. In some embodiments, the method further comprises providing a fifth hairpin monomer.

In some embodiments, the method further comprises providing an initiator comprising the first nucleic acid sequence complementary to the first domain of the first hairpin monomer. In some embodiments, the initiator comprises two domains, wherein each domain is complementary to the first domain of the first hairpin monomer. In some embodiments, three or more molecules of the first hairpin monomer are present on a substrate. In some embodiments, the molecules of the first hairpin monomer are arranged linearly at regular intervals along a nicked DNA duplex.

In some embodiments, the dynamic function is selected from the group consisting of catalytic formation of a branched junction, autocatalytic duplex formation by a cross-catalytic circuit, nucleated dendritic growth, and autonomous locomotion.

In some embodiments, a self-assembly system for performing a dynamic function is provided. The self-assembly system for performing a dynamic function comprises: a first hairpin monomer comprising a first domain comprising a first toehold and a first propagation region, wherein the first toehold is exposed, and wherein the first toehold is located at an end of the monomer; and a second domain comprising a second toehold and a second propagation region, wherein the second toehold is hybridized to a portion of the first propagation region; and a second hairpin monomer.

In some embodiments, the output domain of the second hairpin monomer is complementary to the first domain of the first hairpin monomer. In some embodiments, the self-assembly system further comprises an initiator, wherein the initiator comprises an output domain comprising a third toehold complementary to the first toehold, and wherein the output domain is complementary to the first domain of the first hairpin monomer. In some embodiments, the initiator comprises a second output domain complementary to the first domain of the first hairpin monomer. In some embodiments, three or more molecules of the first hairpin monomer are present on a substrate. In some embodiments, the molecules of the first hairpin monomer are arranged linearly at regular intervals along a nicked DNA duplex.

In some embodiments, the second hairpin monomer comprises an input domain comprising a third toehold and a third propagation region, wherein the third toehold is exposed and complementary to the second toehold of the first hairpin monomer; and an output domain comprising a fourth toehold and a fourth propagation region, wherein the fourth toehold is hybridized to a portion of the third propagation region.

In some embodiments, the self-assembly system further comprises a third hairpin monomer, wherein said third hairpin monomer comprises a second input domain comprising a fifth toehold and a second output domain. Preferably, the fifth toehold is exposed and complementary to the fourth toehold of the output domain of the second hairpin monomer, and a portion of the second output domain is hybridized to a portion of the second input domain. In some embodiments, the second output domain can be complementary to the first domain of the first hairpin monomer. Several embodiments can include additional hairpin monomers.

In some embodiments, the second hairpin monomer further comprises a second output domain comprising a fifth toehold and a fifth propagation region, wherein the fifth toehold is hybridized to a portion of the third propagation region of the input domain of the second hairpin monomer, and the fifth propagation region is single stranded.

In some embodiments, the self-assembly further comprises a third hairpin monomer, wherein the third hairpin monomer comprises: a third input domain comprising a sixth toehold and a sixth propagation region, wherein the sixth toehold is exposed and complementary to the fifth toehold of the second output domain of the second hairpin monomer.

In some embodiments, a method for programming a molecular pathway for carrying out dynamic function is provided. The method comprises: providing a reaction graph representing the molecular pathway for the dynamic function, wherein the reaction graph comprises: an initiator node representing an initiator molecule, wherein said initiator node comprises an initiator port; and at least one monomer node, wherein each monomer node in said set represents a hairpin monomer and comprises: an input port; and at least one output port, wherein each port of a node corresponds to a domain of the corresponding hairpin monomer or initiator molecule, and each domain comprises a toehold, wherein a port is in an accessible state if the toehold of the corresponding domain is exposed, and wherein a port is in an inaccessible state if the toehold of the corresponding domain is sequestered, and wherein the reaction graph indicates each reaction between each node; and translating the reaction graph to hairpin monomers. The reactions between the nodes can be assembly or disassembly reactions, or both.

In some embodiments, the method further comprises: designing nucleic acid primary sequences for the hairpin monomers. In some embodiments the dynamic function is selected from the group consisting of catalytic formation of a branched junction, autocatalytic duplex formation by a cross-catalytic circuit, nucleated dendritic growth, and autonomous locomotion. In some embodiments the reaction graph comprises two or more monomer nodes.

In some embodiments, reaction graph representing a molecular program for a dynamic function is provided. The reaction graph comprises: an initiator node representing an initiator molecule comprising an initiator port; and at least one monomer node, wherein each monomer node represents a hairpin monomer and comprises: an input port; and at least one output port, wherein each port of a node corresponds to a domain of the corresponding hairpin monomer or initiator molecule, and each domain comprises a toehold, wherein a port is in an accessible state if the toehold of the corresponding domain is exposed or in an inaccessible state if the toehold of the corresponding domain is sequestered, and wherein the reaction graph indicates each assembly and/or disassembly reaction between each node.

In some embodiments, an imaging probe is provided. The imaging probe comprises a collection of hairpin monomers comprising a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the collection of hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule, wherein the prescribed shape is imageable. In some embodiments the prescribed shape comprises a 3-dimensional structure that is asymmetric. In some embodiments the prescribed shape comprises a 3-dimensional structure that is detectable by electron cryomicroscopy (ECT).

In some embodiments, the collection of hairpin monomers comprises a first nucleic acid, a second nucleic acid, and a third nucleic acid, wherein the first, second and third nucleic acids each comprise a sequence that allow each to form a hairpin monomer. In some embodiments, the imaging probe further comprises a detectable marker. In some embodiments, the detectable marker is covalently attached to at least one of the first, second, or third nucleic acids. In some embodiments, the detectable marker is a fluorescent protein, such as GFP, RFP, YFP, CFP, or BFP. In some embodiments, the detectable marker is a small molecule fluorophore. In some embodiments, the detectable marker is Fluorescein isothiocyanate (FITC), rhodamine (TRITC), coumarin, Oregon green, eosin, Texas red, cyanine, Nile red, Nile blue, cresyl violet, or oxazine 170.

In some embodiments, one or more of the hairpin monomers comprise an aptamer which binds to a target peptide with specific sub-nanomolar binding affinity. In some embodiments, one or more of the hairpin monomers comprise an aptamer which binds to a target peptide with specific picomolar to micromolar binding affinity.

In some embodiments, a collection of hairpin monomers comprising a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, self-assemble into a binary tree.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers comprising a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the first hairpin monomer is labeled with a first fluorophore, the second hairpin monomer is labeled with a second fluorophore, and the third hairpin monomer is labeled with a third fluorophore, and wherein the collection of hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule. In some embodiments, the prescribed shape is imageable or specifically identifiable. In some embodiments, the collection of hairpin monomers comprises a first nucleic acid, a second nucleic acid, and a third nucleic acid, wherein the first, second, and third nucleic acids each comprise a sequence that allow each to form a hairpin monomer. In some embodiments, the prescribed shape comprises a rigid 3-dimensional structure that arranges the first, second, and third fluorophores in a pattern that is distinguishable from fluorescence attributable to fluorophores not incorporated in the 3-dimensional structure. In some embodiments, the prescribed shape comprises a rigid asymmetric 3-dimensional structure that arranges the first, second, and third fluorophores in a pattern that is distinguishable from fluorescence attributable to fluorophores not incorporated in the 3-dimensional structure.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers comprising a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein one or more of the hairpin monomers bind with high efficiency to at least one peptide tag fused to a fluorescent protein, and wherein the collection of hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers comprising a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the first hairpin monomer is labeled with a first fluorophore, the second hairpin monomer is labeled with a second fluorophore, and the third hairpin monomer is labeled with a third fluorophore, and wherein the collection of hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule, wherein the prescribed shape is imageable.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers that include a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, and at least one fluorescent protein. In some embodiments, it includes a first fluorescent protein fused to a first peptide tag; a second fluorescent protein fused to a second peptide tag; and a third fluorescent protein fused to a third peptide tag; wherein the first peptide tag exhibits specific sub-nanomolar binding affinity for the first hairpin monomer; the second peptide tag exhibits specific sub-nanomolar binding affinity for the second hairpin monomer; and the third peptide tag exhibits specific sub-nanomolar binding affinity for the third hairpin monomer. In some embodiments, it includes a first fluorescent protein fused to a first peptide tag; a second fluorescent protein fused to a second peptide tag; and a third fluorescent protein fused to a third peptide tag; wherein the first peptide tag exhibits specific picomolar to micromolar binding affinity for the first hairpin monomer; the second peptide tag exhibits specific picomolar to micromolar binding affinity for the second hairpin monomer; and the third peptide tag exhibits specific picomolar to micromolar binding affinity for the third hairpin monomer.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers comprising a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the hairpin monomers self-assemble into a trimer comprising the first hairpin monomer, the second hairpin monomer and the third hairpin monomer.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers wherein the hairpin monomers self-assemble into a trimer comprising a first hairpin monomer, a second hairpin monomer and a third hairpin monomer, and wherein the first hairpin monomer is bound to a first peptide tag fused to a first fluorescent protein, the second hairpin monomer is bound to a second peptide tag fused to a second fluorescent protein, and the third hairpin monomer is bound to a third peptide tag fused to a third fluorescent protein.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers wherein a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer self-assemble into a rigid asymmetric 3-dimensional structure comprising the first hairpin monomer bound to the first peptide tag fused to the first fluorescent protein, the second hairpin monomer bound to the second peptide tag fused to the second fluorescent protein and the third hairpin monomer bound to the third peptide tag fused to the third fluorescent protein; wherein the asymmetric 3-dimensional structure arranges the first, second, and third fluorescent proteins in a pattern that is distinguishable from fluorescence attributable to fluorescent proteins not incorporated in the 3-dimensional structure. In some embodiments, the 3-dimensional structure is not asymmetric.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers wherein a first hairpin monomer is triggered into an activated, open conformation upon binding to a target protein.

Some embodiments relate to an imaging probe comprising a collection of 3 to one million hairpin monomers.

Some embodiments relate to an imaging probe comprising a collection of 3 to 50 hairpin monomers.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers wherein a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer self-assemble into a prescribed shape wherein an order of binding between the first hairpin monomer, the second hairpin monomer and the third hairpin monomer determines the prescribed shape.

Some embodiments relate to an imaging probe comprising a collection of hairpin monomers that self-assemble into a prescribed shape, wherein a first hairpin monomer comprises a first fluorescent marker and a second hairpin monomer comprises a second fluorescent marker, and wherein a change from individual hairpin monomers to the prescribed shape results in a structural rearrangement that results in a change in FRET characteristics of at least one fluorescent maker.

Some embodiments relate to a protein organizer comprising a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the first, second, and third hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule, and wherein the first hairpin monomer is linked to a first protein, and wherein the second hairpin monomer is linked to a second protein. In some embodiments, the protein comprises a fluorescent protein.

Some embodiments relate to a protein organizer comprising a collection of hairpin monomers, wherein a first hairpin monomer linked to a first fluorescent protein, a second hairpin monomer linked to a second fluorescent protein, a third hairpin monomer, and a fourth hairpin monomer self-assemble into a four-arm-junction in the presence of a target nucleotide, such that the first fluorescent protein and the second fluorescent protein are co-localized on an end of a duplex arm of the four-arm-junction.

Several embodiments relate to a method for labeling a target with a geometric barcode, comprising providing a collection of hairpin monomers comprising at least a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the first hairpin monomer is labeled with a first fluorophore, the second hairpin monomer is labeled with a second fluorophore, and the third hairpin monomer is labeled with a third fluorophore, and wherein the collection of hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule.

Several embodiments relate to a method for conjugating fluorescent protein with a target molecule, comprising providing a fluorescent protein linked to a peptide adaptor, providing a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the first, second, and third hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule, wherein the first hairpin monomer comprises an aptamer, and wherein the aptamer binds to the fluorescent protein linked peptide adaptor; and combining the fluorescent protein linked to a peptide adaptor and the first hairpin monomer, the second hairpin monomer, and the third hairpin monomer, with a target molecule.

Several embodiments relate to a method for FRET based target detection, comprising providing a first hairpin monomer that is linked to a first fluorescent protein; providing a second hairpin monomer that is linked to a first fluorescent protein; providing a third hairpin monomer that is linked to a second fluorescent protein; providing a fourth hairpin monomer that is linked to a second fluorescent protein, wherein the first, second, third and fourth hairpin monomers autonomously self-assemble into a four-arm-junction in the presence of a target, such that the first fluorescent protein and the second fluorescent protein are co-localized on an end of a duplex arm of the four-arm-junction, thereby altering a FRET signal of the fluorescent proteins.

Several embodiments relate to a method for detecting a target molecule with a geometric structural marker, comprising applying a collection of hairpin monomers comprising a first hairpin monomer and a second hairpin monomer to a sample, wherein the collection of hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule, wherein the prescribed shape is electron dense; detecting the prescribed shape; and using the detected shape as an indicator of the target molecule.

In some embodiments, sufficient hairpin monomers are provided to self-assemble into a tetrahedron.

In some embodiments, nine hairpin monomers that are capable of self-assembly to form a tetrahedron are provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

FIGS. 1 a-f generally depict various aspects of one embodiment for programming biomolecular self-assembly pathways. a, secondary structure of a hairpin monomer. Colored lines represent strand domains; short black lines represent base pairs; arrowheads indicate 3′ ends. The small letters represent sequence segments. b, Secondary structure mechanism illustrating assembly and disassembly reactions during catalytic duplex formation. Letters marked with an asterisk (*) are complementary to the corresponding unmarked letter. c, Abstraction of the motif A as a node with three ports (color/shade use is consistent with a). d, A reaction graph representing a molecular program executed schematically in b and e. e, Execution of the reaction graph of d. f, Hierarchical design process.

FIG. 2 a-f generally depict catalytic self-assembly of three-arm and four-arm branched junctions. The small letters represent sequence segments. Letters marked with an asterisk (*) are complementary to the corresponding unmarked letter. a, Reaction graph for three-arm junctions. b, Secondary structure mechanism. c, Agarose gel electrophoresis demonstrating catalytic self-assembly for the three-arm system with 750-nM hairpins. d, AFM image of a three-arm junction. Scale bar: 10 nm. e, Reaction graph and f, AFM image for a four-arm junction. Scale bar: 10 nm.

FIGS. 3 a-c generally depict autocatalytic duplex formation by a cross-catalytic circuit with exponential kinetics. a, Reaction graph. Multiple assembly arrows entering the same input port depict parallel processes on separate copies of the nodal species. b, Secondary structure mechanism. c, System kinetics examined by fluorescence quenching. Formation of A•B is monitored by the increase in fluorescence resulting from increased spatial separation between the fluorophore resulting from increased spatial separation between the fluorophore (green star in b) and the quencher (black dot in b) at either end of A. Raw data for two independent reactions are displayed for each initiator concentration (20-nM hairpins). Single traces are shown for the controls containing only A and B or only A. Inset: linear fit of the 10% completion time against the logarithm of the relative concentration of I (0.0003×≦[I]≦0.05×). High-concentration end points ([I]≧0.1×) are excluded based on theoretical analysis; low-concentration end points ([I]≦0.001×) are excluded because of signal poisoning by leakage.

FIGS. 4 a-e generally depict triggered assembly of quantized binary molecular trees. a, Reaction graph. Multiple assembly arrows entering the same input port depict parallel processes on separate copies of the nodal species. b, Secondary structure mechanism. c, Agarose gel electrophoresis demonstrating triggered self-assembly. Lanes 1-6: the dominant reaction band shifts with the addition of each generation of hairpins. Subdominant bands are presumed to represent imperfect dendrimers. Lane 7: minimal conversion to reaction products in the absence of initiator. Hairpins A1, A2, B2 at 62.5 nM; the concentration doubles for each subsequent generation of hairpins. Initiator I at 50 nM. d, Linear relationship between amplification signal (putative G5 reaction product) and initiator for three independent experiments (cross, diamond, circle). e, AFM imaging of dendrimers for G=3, 4, and 5.

FIGS. 5 a-f generally depict stochastic movement of a bipedal walker. a, Reaction graph. Bonds between output ports on I and input ports on A represent initial conditions. Static structural elements are depicted by grey line segments. b, Secondary structure mechanism depicting processive locomotion. c-f, Fluorescence quenching experiments measuring the proximity of the quenchers (black dots) on the walker feet to the fluorophores (coloured stars) decorating the track. Fitted curves (solid) are used to determine the time at which the minimum fluorescence (maximum quenching) was observed (dashed vertical line) for each fluorophore. c, Bipedal walker with track labeled by fluorophores JOE (green star)→TAMRA (red)→FAM (blue) as in b. d, Monopedal walkers on the same track (JOE (orange star)→TAMRA (pale green)→FAM (pale blue)). e, Comparison of time scales for bipedal and monopedal walkers (eighteen traces per walker type: three fluorophores, six experiments). f, Bipedal walker with track labeled TAMRA (red star)→JOE (green)→FAM (blue).

FIG. 6 a-f generally depict the procedure for designing the catalytic e-arm junction system. a, the desired dynamic behavior: catalytic formation of a 3-arm DNA junction. b, Reaction graph for catalytic formation of a 3-arm DNA junction. c, Translation of the reaction graph to the secondary structure hairpin monomers. d, Addition of clamping and padding segments. e, Dimensioning. f, Sequence design. Green dot=A (adenine), blue dot=C (cytosine), black dot=G (guanine) and red dot=T (thymine).

FIGS. 7 a-b generally depict execution of the reaction graphs for catalytic 3-arm and 4-arm junction systems. a, Execution of the reaction graph for catalytic 3-arm junction systems. b, Execution of the reaction graph for catalytic 4-arm junction systems.

FIGS. 8 a-d depict catalytic formation of a 4-arm DNA junction. a, Reaction graph. Note: green output ports do not serve as initiators for any downstream reaction, and are omitted here for simplicity. b, Secondary structure schematic of the reaction. c, Agarose gel electrophoresis demonstrates the catalytic formation of the 4-arm junction. d, AFM images of two 4-arm junctions. Scale bar, 10 nm.

FIG. 9 a-b depict AFM measurements of the 3-arm (a) and 4-arm (b) junctions described in FIG. 2 and FIG. 8 a-d. The small images are screenshots of the measurement section files. The distance between the two arrows is listed above the image.

FIG. 10 a-b depict large-field-of-view AFM images of the 3-arm (a) and 4-arm (b) junction systems.

FIGS. 11 a-b depict catalytic formation of a k-arm junction. a, Reaction graph. b, Reaction schematics.

FIG. 12 a-c depict catalytic formation of a 6-arm junction. a, Reaction graph. b and c, Step-by-step reaction schematic.

FIG. 13 depicts the execution of the reaction graph for the autocatalytic system of FIG. 3.

FIG. 14 depicts the detailed reaction schematic for the autocatalytic system of FIG. 3. The length of each segment is 6 nt. Green star, fluorophore; black dot, quencher.

FIG. 15 a-c depict a step-by-step reaction schematic for the autocatalytic system of FIG. 3.

FIG. 16 a-b depict a reaction schematic and stepping gel for the autocatalytic system. a, Reaction schematic. b, Native polyacrylamide gel electrophoresis demonstrates the step-by-step reaction depicted in FIG. 3 b. The symbol ( ) indicates annealing; + indicates 15 minute reaction at room temperature.

FIG. 17 depicts the execution of the reaction graph for the nucleated dendritic growth system.

FIG. 18 depicts a reaction schematic of the nucleated dendritic growth system (part I). Step-by-step reaction schematic of the nucleated dendritic growth system, as described in FIG. 4. The lengths of segments x, x*, and y are 2 nt; the lengths of the other segments are 7 nt. The figure continues in FIG. 19.

FIG. 19 depicts a reaction schematic of the nucleated dendritic growth system (part II). Step-by-step reaction schematic of the nucleated dendritic growth system, as described in FIG. 4. The figure continues from FIG. 9.

FIG. 20 depicts an agarose gel electrophoresis demonstrating quantitative amplification.

FIG. 21 depicts AFM measurements of the G3/G4 dendrimers.

FIG. 22 depicts AFM measurements of the G5 dendrimers.

FIG. 23 depicts large-field-of-view AFM image of the G5 dendrimer system.

FIG. 24 a-b depict execution of the reaction graph for the autonomous walker system of FIG. 5.

FIG. 25 depicts a secondary structure schematic of the walker system of FIG. 5. Stars represent fluorophores; black dots represent quenchers. The lengths of segments a, b, c, and d are 7 nt; the lengths of segments x and y are 2 nt.

FIG. 26 a-b depict the step-by-step secondary structure schematic for the autonomous walker system of FIG. 5. Reaction arrows corresponding to the processive sub-population of walkers are shown in purple.

FIG. 27 a-d depict a detailed secondary structure schematic for step 1 of FIG. 26 a. Reaction arrows corresponding to the processive sub-population of walkers are shown in purple.

FIG. 28 a-b depict assembly of the walker system. a, Assembly procedure. b, Native agarose gel electrophoresis demonstrating the expected assembly of the system.

FIG. 29 a-b depict a fuel system for the walker system. a, Reaction schematic. b, Agarose gel electrophoresis demonstrates catalytic formation of the DNA duplex.

FIG. 30 depicts DNA hairpin synthesis by ligation. The circled P indicates a phosphate group, which is used for ligation by, for example, T4 ligase.

FIG. 31 depicts a schematic of DNA sequences and secondary structures for the catalytic 3-arm junction systems of FIG. 2.

FIG. 32 depicts a schematic of DNA sequences and secondary structures for the catalytic 4-arm junction systems of FIG. 8.

FIG. 33 depicts a schematic of DNA sequences and secondary structures for the autocatalytic system of FIG. 3.

FIG. 34 depicts a schematic of DNA sequences and secondary structures for the nucleated dendritic growth system of FIG. 4.

FIG. 35 depicts a schematic of DNA sequences and secondary structures for the fuels for the walker system of FIGS. 28 a-b and 29 a-b.

FIG. 36 a-c generally depict systems with multiple inputs and outputs. a, Node A has one initially accessible input port which controls three initially inaccessible output ports. b, Node A has an initially accessible pink input port and an initially inaccessible orange input port; these two input ports together control an initially inaccessible output port. c, In general, a node can have m inputs and n outputs.

FIG. 37 generally depict the formation of a 3-dimensional barcode using triggered molecular geometry. a, five hairpin monomers are labeled with four distinct fluorophore tags. b, upon being triggered by a target mRNA, the hairpin monomers self-assemble into a rigid asymmetric structure with four distinct tag positions, forming a 3-dimensional barcode providing both spatial and color information and/or signature.

FIG. 38 a-b depict implementation schemes for a 3-dimensional barcode with 4 distinct tags and 4 differentiable tag positions. a, fluorophore-decorated hairpin monomers co-exist meta-stably in the absence of the target mRNA (T). In the presence of the mRNA target (T), hairpins are triggered to self-assemble into a tetrahedron attached to T. b, hairpin monomers are decorated with a fluorophore and a quencher. The fluorophores and quenchers are positioned such that the fluorophores are quenched in the hairpin configuration. In the presence of the mRNA target (T), hairpins are triggered to self-assemble into a tetrahedron attached to T and the fluorophores are unquenched.

FIG. 39 generally depicts a spatial organizing device (e.g., molecule) for organizing proteins in a prescribed spatial pattern.

FIG. 40 a depicts a fluorescent protein (FP)-hairpin complex comprising a fluorescent protein fused to a peptide adapter, which is conjugated to an aptamer-modified hairpin.

FIG. 40 b 1-b 4 depict four schemes for triggered protein (including FP) organizers. b 1, Meta-stable FP-hairpins are conjugated to a single species of FP and triggered by the target mRNA to self-assemble into a binary “tree”. In some embodiments, the tree has a specific color signature. In some embodiments, the tree is all (or primarily all) of the same color of fluorophore. b 2, Presence of a mRNA target catalyzes a set of three metastable hairpins conjugated to distinct color FPs to form a trimer. b 3, Presence of a mRNA target catalyzes 2 sets of hairpins monomers modified at the 5′ and 3′ ends of with aptamers that bind to same color FPs to self-assemble into a four-arm junction, such that upon the formation of the cross structure, two distinct color FPs are co-localized on the same end of a DNA duplex arm of the 4-arm junction, resulting in a FRET pair. b 4, Presence of a mRNA target catalyzes the formation of a tetrahedron with FP-decorated vertices.

FIG. 41 generally depicts some embodiments for the formation of a triggered geometric marker attached to a target protein for imaging by electron cryotomography (ECT).

FIG. 42 a depicts some schemes for implementing a triggered geometric marker device. The target protein is fused to a peptide tag/adaptor that binds to a nucleic acid aptamer (Step 1). Nucleic acid hairpin monomers are introduced and triggered to self-assemble into a geometric shape attached to the tail of the aptamer (Step 2).

FIG. 42 b depicts some schemes for implementing a triggered geometric marker device utilizing a switchable nucleic acid aptamer. The target protein is fused to a peptide tag/adaptor that binds to a nucleic acid aptamer, which triggers the switchable aptamer to assume an activated, open configuration. Nucleic acid hairpin monomers self-assemble into a geometric shape attached to the tail of the activated aptamer.

FIG. 43 a-d generally depict embodiments for the catalytic formation of a DNA tetrahedron. a, Initiator molecule and secondary structure of metastable hairpin monomers. b, Partial tetrahedral structure comprising the three-arm junction and connecting monomers. c, Partial tetrahedral structure comprising the three-arm junction and connecting monomers with partial binding of complementary segments. d, Partial tetrahedral structure comprising the three-arm junction and connecting monomers with full binding of complementary segments. The small letters represent sequence segments. Letters marked with an asterisk (*) are complementary to the corresponding unmarked letter.

DETAILED DESCRIPTION

Various embodiments disclosed herein are generally directed towards programming biomolecular self-assembly pathways to form molecules with characteristics and/or “signatures” that can be used as imaging probes. This can include fluorescent barcode arrangements, which can include, for example, synthetic fluorophores or genetically encoded fluorophores (such as GFP), as well as structural arrangements, so that identification of a specific three- or two-dimensional shape will indicate the presence of a target of interest.

The difficulty of engineering molecular machines or structures capable of nanoscale autonomous assembly or locomotion has attracted significant interest in recent years. Yin, P. et al., Angew. Chem. Int. Ed. 43, 4906-4911 (2004); Tian, Y. et al., Angew. Chem. Int. Ed. 44, 4355-4358 (2005); Bath, J. et al., Angew. Chem. Int. Ed. 44, 4358-4361 (2005); Pei, R. et al., J. Am. Chem. Soc. 128, 12693-12699 (2006); Venkataraman et al., Nat. Nanotechnol. 2, 490-494 (2007). Previous attempts to rationally encode structure and function into synthetic amino and nucleic acid sequences have largely been limited to engineering molecules that self-assemble into prescribed target structures without explicit concern for transient system dynamics. For example, previously, DNA dendrimer target structures have been synthesized via sequential ligation of structural subunits (Li, Y. et al. Nat. Mater. 3, 38-42 (2004)). However, the methods and compositions described herein make it possible to encode dynamic function in the design space of biomolecules.

A new approach to diverse molecular self-assembly pathways has been developed based on the rewiring of complementarity relationships between modular domains in a versatile hairpin motif. Monomer and polymer sequences can be encoded with the reaction pathways by which self-assembly occurs. In some embodiments this allows them to perform dynamic functions without human intervention. By programming complementarity relationships between domains within the hairpin motif, systems can be engineered to exhibit a wide variety of dynamic behaviors. The modular programmability of the hairpin motif can be used to facilitate the conversion of conceptual dynamical system designs into physical molecular implementations, enabling new approaches to fabrication, amplification, and transport (see, Yin et al., Nature 451(7176), 318-322; Supplementary Information pages 1-49 (2008), which is incorporated herein by reference in its entirety).

The versatile hairpin motif can be used to implement a variety of dynamic functions through self-assembly pathways. In some embodiments, starting from a conceptual dynamic function, a molecular implementation can be realized in three steps: (1) pathway specification via a “reaction graph”; (2) translation of the reaction graph into a secondary structure mechanism using monomers having the hairpin motif (“hairpin monomers”); and (3) computational design of hairpin monomer primary sequences.

Methods and compositions for programming biomolecular self-assembly pathways for dynamic functions, including, without limitation, molecular programming of catalytic geometry, catalytic circuitry, nucleated dendritic growth and autonomous locomotion are provided. In some embodiments, hairpin monomers to implement various dynamic functions are provided. In some embodiments, methods for designing hairpin monomers to implement dynamic functions are provided. In various embodiments, compositions and methods are provided for systems with catalytic geometry, catalytic circuitry, nucleated dendritic growth or autonomous locomotion.

One embodiment for programming a biomolecular self-assembly pathway is summarized in FIG. 1 f. As shown in FIG. 1 f, beginning with the dynamic function of, for example, the catalytic formation of a DNA duplex, a reaction graph using nodal abstractions is specified (step (1)). Next, the reaction graph is translated into motifs. In particular, hairpin monomers are designed encompassing the second structure mechanism of the functions provided by the reaction graph (step (2)). Then the primary sequences of the hairpin monomers are designed (step (3)).

A schematic depiction of the secondary structure of a hairpin monomer, which embodies the versatile hairpin motif, according to various embodiments disclosed herein is shown in FIG. 1 a. The hairpin monomer (A) shown in FIG. 1 a comprises three concatenated domains, a, b, and c. In some embodiments, monomers can comprise two or more concatenated domains. In preferred embodiments, each domain has a nucleation site called a toehold. For example, in FIG. 1 a the toeholds are denoted a_(t), b_(t), and c _(t), respectively. Preferably, a domain further comprises a propagation region. In some embodiments, the propagation region can be the portion of a domain that is not the toehold. Typically, a hairpin monomer comprises at least one input domain, and at least one output domain. In some embodiments, the input domain can be an initiator binding domain. For example, in FIG. 1 a, domain a of hairpin monomer A is an initiator binding domain. In some embodiments, an output domain can be an assembly domain or a disassembly domain. For example, in FIG. 1 b, domain b of hairpin monomer A is an assembly domain, and in domain a* of hairpin monomer B is a disassembly domain.

Two basic reactions can be programmed using the hairpin motif, as illustrated for one possible example of catalytic duplex formation in FIG. 1 b. The reaction in FIG. 1 b utilizes two hairpin monomers, A and B, each having two concatenated domains, a and b. First, an assembly reaction (1) occurs when a single-stranded initiator I, containing an exposed toehold a_(t)*, nucleates at the exposed toehold a_(t) of input domain a (also called the “initiator binding domain”) of hairpin monomer A, initiating a branch migration that opens the hairpin. Hairpin output domains b and c, with newly exposed toeholds b_(t) and c_(t), can then serve as assembly initiators for other suitably defined hairpins, permitting cascading (e.g., in reaction (2), output domain b (an “assembly domain”) of hairpin monomer A assembles with input domain b* (an “assembly complement domain”) of hairpin monomer B, opening the hairpin). Second, a disassembly reaction (3) occurs when a single-stranded output domain a* of B (a “disassembly domain”) initiates a branch migration that displaces the initiator I from A. In this example, I catalyzes the formation of duplex A•B via a prescribed reaction pathway.

To assist in programming more complex reaction pathways, a hairpin monomer can be abstracted as a node with input and output ports, with the state of the ports being indicated as either accessible or inaccessible. For example, the hairpin monomer of FIG. 1 a can be abstracted as a node with three ports (FIG. 1 c): a triangular input port and two circular output ports. The shade/color use for the nodal abstraction in FIG. 1 c is consistent with FIG. 1 a. The state of each port is either accessible (open triangle/circle) or inaccessible (solid triangle/circle), depending on whether the toehold of the corresponding hairpin domain is exposed or sequestered. Functional relationships between ports within a node are implicit in the definition of the nodal abstraction corresponding to a particular motif (e.g., for the node of FIG. 1 c, the output ports flip to accessible states if the input port is flipped to an inaccessible state through an interaction with a complementary upstream output port).

Depicting assembly reactions by, for example, solid arrows and disassembly reactions by dashed arrows (each directed from an output port to a complementary input port of a different node), reaction pathways can be specified abstractly in the form of a reaction graph, representing a program to be executed by molecules such as, for example, nucleic acid molecules.

A reaction graph provides a simple representation of assembly (and disassembly) pathways that can be translated directly into molecular executables: nodes represent motifs, ports represent domains, states describe accessibility, arrows represent assembly and disassembly reactions between complementary ports. For example, the reactions depicted in the secondary structure mechanism of FIG. 1 b are specified using a reaction graph in FIG. 1 d. Conventions for the reaction graphs disclosed herein are provided below. The initial conditions for the program are described via the state (accessible or inaccessible) of each port in a reaction graph. FIG. 1 e depicts the execution of this reaction graph through cascaded assembly and disassembly reactions. An assembly reaction is executed when ports connected by a solid arrow are simultaneously accessible.

The hairpin monomer functions as a modular programmable kinetic trap, and rewiring the connections between nodes in the reaction graph corresponds to rewiring the connections between kinetic traps in the underlying free energy landscape. In the physical systems, metastable hairpins are initially caught in engineered kinetic traps; the introduction of initiator molecules begins a chain reaction of kinetic escapes in which the hairpin species interact via programmed assembly and, optionally, disassembly steps to implement dynamic functions. Preferably, the time scale of metastability for kinetically trapped molecules is longer than the time scale relevant for the execution of the program.

As will be appreciated by one of skill in the art, the ability to design and implement biomolecular self-assembly (and disassembly) pathways can have great benefit, especially for engineering functional mechanical systems at the molecular scale. For example, the methods and compositions disclosed herein are beneficial for, inter alia, smart materials (e.g., artificial drugs and self-healing structures), nanosensors (e.g., photosensors), nanofacturing, nanorobots (e.g., replicating nanorobots and medical nanorobots), utility fog, and phased-array optics. In some embodiments, methods and compositions disclosed herein are beneficial for providing, for example without limitation, smart therapeutics that can detect a disease marker (e.g., mutant mRNA known to cause cancer) and then activate a therapeutic biological pathway (e.g., kill the cancer cell leaving healthy cells untouched).

The above and additional embodiments are discussed in more detail below, after a brief discussion of the definitions some of the terms used in the specification.

DEFINITIONS

The section headings used herein are for organizational purposes only and are not to be construed as limiting the described subject matter in any way. All literature and similar materials cited in this application, including but not limited to, patents, patent applications, articles, books, treatises, and internet web pages are expressly incorporated by reference in their entirety for any purpose. When definitions of terms in incorporated references appear to differ from the definitions provided in the present teachings, the definition provided in the present teachings shall control. It will be appreciated that there is an implied “about” prior to the temperatures, concentrations, times, etc discussed in the present teachings, such that slight and insubstantial deviations are within the scope of the present teachings herein. In this application, the use of the singular includes the plural unless specifically stated otherwise. Also, the use of “comprise”, “comprises”, “comprising”, “contain”, “contains”, “containing”, “include”, “includes”, and “including” are not intended to be limiting. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive.

Unless otherwise defined, scientific and technical terms used herein shall have the meanings that are commonly understood by those of ordinary skill in the art. Further, unless otherwise required by context, singular terms shall include pluralities and plural terms shall include the singular. Generally, nomenclatures utilized in connection with, and techniques of, cell and tissue culture, molecular biology, and protein and oligo- or polynucleotide chemistry and hybridization described herein are those well known and commonly used in the art. Standard techniques are used, for example, for nucleic acid purification and preparation, chemical analysis, recombinant nucleic acid, and oligonucleotide synthesis. Enzymatic reactions and purification techniques are performed according to manufacturer's specifications or as commonly accomplished in the art or as described herein. The techniques and procedures described herein are generally performed according to conventional methods well known in the art and as described in various general and more specific references that are cited and discussed throughout the instant specification. See, e.g., Sambrook et al., Molecular Cloning: A Laboratory Manual (Third ed., Cold Spring Harbor Laboratory Press, Cold Spring Harbor, N.Y. 2000). The nomenclatures utilized in connection with, and the laboratory procedures and techniques of described herein are those well known and commonly used in the art.

As utilized in accordance with the embodiments provided herein, the following terms, unless otherwise indicated, shall be understood to have the following meanings:

A “self-assembly pathway” is a series of reactions autonomously executed by monomers in the formation of a polymer. The self-assembly pathway comprises assembly, or polymerization, of monomers. In some embodiments, the self-assembly pathway can also comprise one or more disassembly reactions.

The term “nucleic acid” refers to natural nucleic acids, artificial nucleic acids, analogs thereof, or combinations thereof. Nucleic acids can also include analogs of DNA or RNA having modifications to either the bases or the backbone. For example, nucleic acid, as used herein, includes the use of peptide nucleic acids (PNA). The term “nucleic acids” also includes chimeric molecules.

The term “hairpin” as used herein refers to a structure formed by intramolecular base pairing in a single-stranded polynucleotide ending in an unpaired loop (the “hairpin loop”). In various embodiments, hairpins comprise a hairpin loop protected by stems. For example, a hairpin can comprise a first stem region, a hairpin loop region, and a second stem region. The first and second stem regions can hybridize to each other and together form a duplex region. In some embodiments, the hairpin can comprise a first stem region, a first hairpin loop region, a second stem region, a second hairpin loop region, and a third stem region. The second stem region can hybridize to a complementary portion of the first stem region and a complementary portion of the second stem region to form two duplex regions. Thus, a stem region of a hairpin monomer is a region that hybridizes to a complementary portion of the same monomer to form the duplex stem of a hairpin.

The term “hairpin loop” refers to a single stranded region that loops back on itself and is closed by a single base pair.

“Interior loop” and “internal loop,” are used interchangeably and refer to a loop closed by two base pairs. The closing base pairs are separate by single stranded regions of zero or more bases. A “bulge loop” is an interior loop where one of the separated single-stranded regions is zero bases in length and the other is greater than zero bases in length.

An “initiator” is a molecule that is able to initiate the polymerization of monomers. Preferred initiators comprise a nucleic acid region that is complementary to the initiator binding domain of a monomer.

“Monomers” as used herein refers to individual nucleic acid oligomers. Typically, at least two monomers are used in self-assembly pathways, although three, four, five, six or more monomers can be used. Typically each monomer comprises at least one domain that is complementary to at least a portion of one other monomer being used for the self-assembly pathway. Monomers are discussed in more detail below. In some embodiments, a monomer can have a hairpin motif. A monomer having a hairpin motif is referred to as a “hairpin monomer.” In some embodiments, a monomer can be an initiator.

The term “domain” refers to a portion of a monomer comprising a sequence. Preferably, a domain of a hairpin monomer comprises a toehold and a propagation region. An “input domain” of a monomer refers to a domain that is configured to receive a signal which initiates a physical and/or chemical change, such as, a for example, a conformational change, of the monomer. Preferably, the signal is binding of a complementary sequence to the domain, typically beginning at the toehold. In some embodiments, an input domain can be an initiator binding domain, an assembly complement domain, or a disassembly complement domain. An “output domain” of a monomer refers to a domain that is configured to confer a signal. Preferably, the signal is binding of a complementary sequence to an input domain. In some embodiments, an output domain is configured to confer a signal to an input domain of another monomer. In some embodiments, an output domain can be, for example, an assembly domain, or a disassembly domain. In some embodiments, an output domain can be present in an initiator.

A first monomer in a self-assembly pathway preferably has an initiator binding or input domain (e.g., domain a of monomer A in FIG. 1 a) that is complementary to a portion of an initiator. The initiator binding domain preferably has an exposed toehold. Binding of the initiator to the initiator binding domain initiates the self-assembly pathway. An initiator binding domain is an input domain.

A monomer preferably has at least one output domain (e.g., domain b of monomer A in FIG. 1 a) that is complementary to an input domain of another monomer. An output domain on a hairpin monomer is preferably only available to interact with the input domain of the other monomer when a self-assembly pathway has been started by the initiator. For example, the assembly domain of a first monomer becomes available to hybridize to the assembly complement domain of a second monomer when the first monomer has already hybridized to at least a portion of an initiator, as discussed in more detail below.

The term “nucleate” as used herein means to begin a process of, for example, a physical and/or chemical change at a discrete point in a system. The term “nucleation” refers to the beginning of physical and/or chemical changes at discrete points in a system. In some embodiments, nucleation of a self-assembly reaction can occur by, for example, the hybridization of a portion of an initiator to an exposed toehold of a hairpin monomer.

The term “toehold” refers to nucleation site of a domain comprising a nucleic acid sequence designed to initiate hybridization of the domain with a complementary nucleic acid sequence. The secondary structure of a monomer can be such that the toehold is exposed or sequestered. For example, in some embodiments, the secondary structure of the toehold is such that the toehold is available to hybridize to a complementary nucleic acid (the toehold is “exposed,” or “accessible”), and in some embodiments, the secondary structure of the toehold is such that the toehold is not available to hybridize to a complementary nucleic acid (the toehold is “sequestered,” or “inaccessible”). If the toehold is sequestered or otherwise unavailable, the toehold can be made available by some event such as, for example, the opening of the hairpin of which it is a part of. When exposed, a toehold is configured such that a complementary nucleic acid sequence can nucleate at the toehold. In some embodiments, nucleation of a complementary nucleic acid sequence at an exposed toehold initiates branch migration that opens up the hairpin of a hairpin monomer.

A “propagation region” as used herein refers to a portion of a domain of a hairpin monomer that is configured to hybridize to a complementary nucleic acid sequence of another hairpin monomer once the toehold of the domain nucleates at an exposed toehold of the other hairpin monomer. The propagation region of a hairpin monomer is configured such that an available complementary nucleic acid sequence does not nucleate at the propagation region; rather, the propagation region hybridizes to a complementary nucleic acid sequence only after nucleation at the toehold of the same domain.

In some embodiments, monomers can be “metastable.” That is, in the absence of an initiator they are kinetically disfavored from associating with other monomers comprising complementary regions.

As used herein, the terms “polymerization” and “assembly” are used interchangeably and refer to the association of two or more monomers, or one or more monomers and an initiator, to form a polymer. The “polymer” can comprise covalent bonds, non-covalent bonds or both. For example, in some embodiments three species of monomers can hybridize sequentially to form a polymer comprising a three-arm branched junction.

As used herein term “disassembly” refers to the disassociation of an initiator or at least one monomer from a polymer or another monomer. For example, polymers can disassemble from polymers, and monomers can disassemble from polymers.

As used herein “reaction graph” refers to a representation of assembly (and, optionally, disassembly) pathways that can be translated into molecular executables.

As used herein the terms “flip” and “switch” are used interchangeably and refer to a change from one state (e.g., accessible) to another state (e.g., inaccessible).

As used herein, an “aptamer” is an oligonucleotide that is able to specifically bind an analyte of interest other than by base pair hybridization. Aptamers typically comprise DNA or RNA or a mixture of DNA and RNA. Aptamers can be naturally occurring or made by synthetic or recombinant means. The aptamers are typically single stranded, but can also be double stranded or triple stranded. They can comprise naturally occurring nucleotides, nucleotides that have been modified in some way, such as by chemical modification, and unnatural bases, for example 2-aminopurine. See, for example, U.S. Pat. No. 5,840,867. The aptamers can be chemically modified, for example, by the addition of a label, such as a fluorophore, or a by the addition of a molecule that allows the aptamer to be crosslinked to a molecule to which it is bound. Aptamers are of the same “type” if they have the same sequence or are capable of specific binding to the same molecule. The length of the aptamer will vary, but is typically less than about 100 nucleotides.

As used herein a “signature” denotes that some characteristic of a molecule is identifiable for that specific molecule. In some embodiments, the signature is unique, so that the presence of the signature will let someone know that a particular species, genus, or subgenus of molecules is present. Signatures can be fluorescent in nature (e.g., a combination of one or more specific fluorophores to provide specific fluorescence spectra, quenching aspects, etc.) In some embodiments, the signature is structural in nature, such as a specific two or three dimensional shape, which can be detected either directly or indirectly. A barcode is one example of a signature.

The term “fluorophore” refers to any type of fluorescent molecule or compound used to mark proteins, tissues, and cells with a fluorescent label for examination by fluorescence microscopy. Fluorophores can be fluorescent proteins (FPs) or fluorescent small molecules. Examples of fluorescent proteins include, but are not limited to: green fluorescent protein (GFP), enhanced green fluorescent protein (EGFP), Emerald, Superfolder GFP, Azami Green, mWasabi, TagGFP, TurboGFP, AcGFP, ZsGreen, T-Sapphire, blue fluorescent protein (BFP), enhanced fluorescent protein (EBFP), EBFP2, Azurite, mTagBFP, cyan fluorescent protein (CFP), enhanced cyan fluorescent protein (ECFP), Cerulean, CyPet, AmCyan1, Midori-Ishi Cyan, TagCFP, mTFP1 (Teal), yellow fluorescent protein (YFP), enhanced yellow fluorescent protein (YFP), Topaz, Venus, mCitrine, YPet, TagYFP, PhiYFP, ZsYellow1, mBanana, orange fluorescent protein (OFP), Kusabira Orange, Kusabira Orange2, mOrange, dTomato, mTangerine, red fluorescent proteins (RFP), DsRed, mRuby, mApple, mStrawberry, AsRed2, JRed, mCherry, HcRed1, mRaspberry, dKeima-Tandem, HcRed-Tandem, mPlum, and AQ143. Examples of fluorescent small molecules include, but are not limited to: fluorescein isothiocyanate (FITC), rhodamine (TRITC), coumarin, Oregon green, eosin, Texas red, cyanine, Nile red, Nile blue, cresyl violet, and oxazine 170.

The term “fluorescent geometric barcode” refers to any structure formed from the self-assembly of three or more hairpin monomers, which arranges fluorophores associated with the hairpin monomers in a prescribed pattern. In some embodiments, the structure is asymmetric.

The term “protein organizer” refers to any structure formed from the self-assembly of three or more hairpin monomers associated with one or more proteins, which arranges the proteins in a prescribed pattern. In some embodiments, the structure is asymmetric.

By “three-dimensional structure” what is meant is that the structure has a component that structurally extends out of a plane. While it will be appreciated that long lengths of nucleic acids and even hairpin structures could be argued to be “three-dimensional structures”, such structures are not encompassed within the term “three-dimensional” as used herein. Rather, what is meant is that the structure's arms (assuming them to be rigid) extends not only in a X and Y direction, but also in a direction Z, which is perpendicular to X and Y. That is not to say that the arm itself must be rigid or must be perpendicular, but that it extends in that perpendicular direction. In some embodiments, assuming the arms of the structure are rigid, a structure will be considered three-dimensional if it must extend in three dimensions. In some embodiments, a structure is three-dimensional when a single plane defined by the hairpin monomers cannot contain structure. In some embodiments, a structure is three-dimensional when the running lengths of the hairpin monomers or nucleic acids define a first dimension, a second dimension that is at least partially perpendicular to the first dimension (e.g., a plane) and a third dimension, that is at least partially perpendicular to the first and second dimensions. As will be appreciated by those of skill in the art, the thickness of the hairpin monomer or nucleic acids themselves are not considered when determining whether or not a structure is three-dimensional, as the term is used herein. In some embodiments, a first hypothetical line (X) down the length of a first hairpin monomer and a second hypothetical line (Y) down the length of a second hairpin monomer can define a first plane (e.g., limit and define a plane X and Y). In such embodiments, a third hypothetical line (Z) down the length of a third hairpin monomer, where the first and second lines are perpendicular to the third line, can define the structure as being a three-dimensional structure. In many embodiments, more than three lengths or arms will be required to make the structure a rigid three dimensional structure (e.g., 6 arms or more for some embodiments).

In some embodiments, “complementarity” can be perfect complementarity. In some embodiments, “complementarity” simply denotes that the sequences are complementary enough to allow for selective self-hybridization, and selective opening into the larger two or three dimensional structure, for a given purpose.

The term “closed structure” denotes that at least one structural element of a denoted nucleic acid structure has been closed to form, for example, a closed loop or other closed arrangement. Not all of the parts in the system need be closed. In some embodiments, the structure defines a closed volume structure, such as a three dimensional triangle, pyramid, cube, etc. In some embodiments, the arms of the self-assembled structure define a perimeter of the three-dimensional shape.

System Design

Starting from a conceptual dynamic function, molecular implementation of a self-assembly pathway can be realized in three steps as summarized in, for example, FIG. 1 f.

Step 1: Pathway specification. In some embodiments, the pathway that implements a target dynamic function can be specified using a reaction graph, discussed in detail below. A reaction graph provides a simple representation of assembly (and disassembly) pathways that can be translated into molecular executables. For example, nodes in the reaction graph represent hairpin monomers, ports of the nodes represent domains, states of the ports describe accessibility, and arrows between the nodes represent assembly and disassembly reactions between complementary ports. An assembly reaction is executed when ports connected by a solid arrow are simultaneously accessible.

Step 2: Translation to motifs. The reaction graph can be directly translated to hairpin monomer secondary structures. In other words, hairpin monomer secondary structures can be modeled and designed based on the nodes and functional relationships represented in the reaction graph. For example, a node in a reaction graph can be translated into a hairpin monomer. The ports on the node can be translated into the domains of the hairpin monomer. More particularly, an input port on a node can be translated into an input domain of a hairpin monomer, and an output port can be translated into an output domain. The functional relationships between the nodes in the reaction graph can be translated into the functionality of the domains of the hairpin monomer. Initial dimensioning of the number of nucleotides in each segment can be performed using, for example, the NUPACK server, which models the behavior of strand species in the context of a dilute solution. Dirks et al., SIMA Rev. 49, 65-88 (2007). Several examples of hairpin monomer secondary structure design based on a reaction graph are provided below.

Step 3: Sequence design. The composition of the monomers is not limited to any particular sequences or number of bases, and is designed based on the particular dynamic function. A number of criteria can be used to design the monomers to achieve the desired properties. These include, for example and without limitation, sequence symmetry minimization, the probability of adopting the initiator secondary structure at equilibrium, the average number of incorrect nucleotides at equilibrium relative to the target structure, and hybridization kinetics. In some embodiments, primary sequences of the hairpin monomers can be designed by considering a suite of structures that punctuate the intended reaction pathway. In some embodiments, structures that explicitly preclude undesired off-pathway interactions (e.g., structures specifying the absence of an interaction between two strands that should not pair) are considered in designing the hairpin monomers.

In some embodiments, the sequences can be optimized computationally to maximize affinity and specificity for a desired structure by minimizing the average number of incorrectly paired bases at equilibrium (Dirks et al., Nucleic Acids Research, 32:1392-1403, 2004.) In some embodiments, the optimization can be performed primarily by computer software. (R. M. Dirks and N. A. Pierce. Nucleic acid sequence design software, unpublished. 2007. J. N. Zadeh and N. A. Pierce. Multi-objective nucleic acid sequence design software, unpublished. 2007.) In some embodiments, further manual optimization based on the same design metric can be performed for a subset of crucial target structures. Monomers are described in detail below. Several examples of hairpin monomer primary sequence design based on secondary structure are provided below.

The thermodynamic behavior of the sequences can be further analyzed using, for example, the NUPACK server (www.nupack.org). (Dirks et al., SIAM Rev, 49-65-88, 2007; Zadeh et al., NUPACK: a web-based tool for the analysis and design of nucleic acid systems. In preparation, 2007.) Stochastic kinetic simulation (Flamm et al., RNA, 6:325-338, 2000) can also be performed to confirm the absence of significant kinetic traps along the target reaction pathways. (J. M. Schaeffer and E. Winfree. Multi-stranded kinetic simulation software, unpublished).

The physical self-assembly pathway system components (e.g., hairpin monomers) can be prepared using standard methods, including, for example, commercially available nucleic acid synthesizers or obtained from commercial sources such as Integrated DNA Technologies (Coralville, Iowa). The monomers and polymers can be verified using, for example and without limitation, gel electrophoresis, bulk fluorescence quenching, or single-molecule atomic force microscopy (AFM), discussed below.

Reaction Graph Conventions

This section provides conventions for the reaction graphs described and depicted herein. Of course, as will be appreciated by those of skill in the art, reaction graphs representing the self-assembly pathways described herein can be prepared using conventions other than those described below to achieve the same results.

Initial conditions. The initial condition of the system is defined by the state of each port and the initial bonds between the ports. An initial bond between an output port and an input port implies that an assembly reaction has already occurred prior to the execution of the reaction graph (see, e.g., the bond between the output port of I and the input port of A in FIG. 5 a).

Static structural elements. Static structural elements are depicted by gray line segments (e.g., the substrate of FIG. 5 a) and are inert during execution of the reaction graph. These elements can be used to impose geometric constraints on the execution of the reaction graph (e.g., the rigid substrate and inextensible torso of the walker system).

Execution starting points. Execution begins with any solid arrow (assembly reaction) connecting two accessible ports. In a system lacking two accessible ports connected by a solid arrow, execution cannot begin (e.g., the removal of node I can prevent execution of the pathway).

Assembly reaction. An assembly reaction is depicted by a solid arrow that points from an input port to a complementary output port of a different node. An assembly reaction is executed when these two ports are simultaneously accessible. In the execution of an assembly reaction, a bond is formed between the two ports, they are flipped to their inaccessible states, and the internal logic of the node with the affected input port is applied to its output ports (e.g., for the present motif, the output ports are flipped to their accessible states). Multiple solid arrows entering the same input port depict parallel processes on separate copies of the nodal species (e.g., the input port of node A in FIG. 3 a and the input ports of nodes A2-A5 and B2-B5 in FIG. 4 a).

Disassembly reaction. A disassembly reaction is depicted by a dashed arrow that points from an input port to a complementary output port of a different node. Using nodal abstractions of the present hairpin motif, a disassembly arrow completes a disassembly cycle. For a cycle involving k nodes: input port 1∘blue output port 2→input port 3∘blue output port 4 . . . blue output port 2k

input port 1, where → denotes and assembly reaction,

denotes a disassembly reaction, and ∘ denotes the internal logical connection between two ports on the same node. For example, FIG. 1 d contains a disassembly cycle for k=2: input port of A ∘ blue output of A→input port of B ∘ blue output port of B

input port of A. FIG. 2 a contains a disassembly cycle for k=3: input port of A ∘ blue output of A→input port of B ∘ blue output port of B→input port of C ∘ blue output port of C

input port of A. In physical terms, the displacing strand and the strand to be displaced emanate as adjacent branches for a k-arm junction, allowing nucleation of the displacement branch migration (e.g., FIG. 2 b). The special case of k=2 corresponds to standard toehold-mediate strand displacement (e.g., FIG. 1 b, where the whole of domain b of hairpin A serves as the toehold). Yurke et al., Nature 406, 605-608 (2000).

A disassembly reaction is executed when the participating output port is accessible and the participating input port is inaccessible (using nodal abstractions of the present motif, a disassembly arrow completes a disassembly cycle implies that the participating output port can only become accessible after the participating input port becomes inaccessible).

In the execution of a disassembly reaction (e.g., FIG. 1 e), the existing bond from an (inaccessible) output port to an (inaccessible) input port is replaced by a new bond to the displacing (accessible) output port; the states of both output ports are flipped.

Multiple dashed arrows entering the same input depict parallel disassembly cycles involving separate copies of the nodal species.

Reaction graphs can be extended beyond the present versatile motif by defining new nodal species that abstract the functional relationships between domains in other motifs. In some embodiments, the present hierarchical approach to rationally encoding dynamic function in nucleic acid sequences can be used in, for example, constructing a compiler for biomolecular function—an automated design process uses a modular conceptual system design as an input, and provides a set of biopolymer sequences that encode the desired dynamic system behavior as an output.

Nodal Abstractions

As discussed above, to assist in programming more complex reaction pathways, a hairpin monomer can be abstracted as a node with input and output ports, with the state of the ports being indicated as either accessible or inaccessible. For example, the hairpin monomer of FIG. 1 a can be abstracted as a node with three ports (FIG. 1 c): a triangular input port and two circular output ports. The color use for the nodal abstraction in FIG. 1 c is consistent with FIG. 1 a. The state of each port is either accessible (open triangle/circle) or inaccessible (solid triangle/circle), depending on whether the toehold of the corresponding hairpin domain is exposed or sequestered. Of course, the particular conventions used for the nodal abstractions can vary from those disclosed herein and achieve the same result. An initiator can also be abstracted as a node with an input port, with the state of the port being indicated as either accessible or inaccessible. In some embodiments, the node representing an initiator can be referred to as an initiator node. In some embodiments, the node representing an initiator can be referred to as an initiator node. In some embodiments, nodes can have multiple input ports and/or multiple output ports.

In the nodal abstractions, nodes represent hairpin monomers and initiators, ports represent domains, and the port states describe accessibility of the corresponding domains. For example, an input port represents an input domain, and an output port represents and output domain. In addition, an accessible port represents an exposed (accessible) domain, and an inaccessible port represents a sequestered (inaccessible) domain.

Functional relationships between ports within a node are implicit in the definition of the nodal abstraction corresponding to a particular motif (e.g., for the node of FIG. 1 c, the output ports flip to accessible states if the input port is flipped to an inaccessible state through an interaction with a complementary upstream output port).

In some embodiments, nodal abstractions can be used in a reaction graph to model a dynamic function. Secondary structure mechanisms can then be modeled and designed based on the reaction graph. Hairpin monomer (and initiator) primary sequences can be designed from the secondary structure mechanisms.

Nodes having multiple input and output ports are shown in FIG. 36 a-c. In FIG. 36 a, node A has one initially accessible input port which controls three initially inaccessible output ports. It implements the molecular logic: if A's input is rendered inaccessible by the arrival of node I, then make all the three output ports accessible. The right panel depicts the molecular implementation using the hairpin motif. In FIG. 36 a, toehold a_(t) is initially accessible, while toeholds b_(t), c_(t), and d _(t) are inaccessible. Initiator I can hybridize with A and opens the hairpin, rendering toeholds b_(t), c_(t), and d _(t) accessible. In FIG. 36 b, node A has an initially accessible pink input port and an initially inaccessible orange input port; these two input ports together control an initially inaccessible output port. It implements the molecular logic: if both of A's output ports are rendered inaccessible by the arrivals of nodes I1 and I2, then make the output port accessible. The right panel depicts the molecular implementation using the hairpin motif. In FIG. 36 b, toeholds a1 _(t) is initially accessible; toehold a2 _(t) is initially inaccessible; toehold b_(t) is initially inaccessible. Initiator I1 can hybridize with A, and renders a2 _(t) accessible; then the now accessible a2 _(t) can hybridize with I2, which opens the hairpin, rendering toehold b_(t) accessible. Generally, a node can have m inputs and n outputs (FIG. 36 c). In preferred embodiments, at least one of the input ports is initially accessible; all the output ports are initially inaccessible.

The node implements a prescribed molecular logic such that only a prescribed combination or combinations of suitable activators can activate a corresponding combination of output ports. For example, if and only upon hybridizing with initiators I1 AND (I2 OR I3) but NOT (I4 OR I5), activates output ports (O1 AND O2 AND O4).

Reaction graphs

Self-assembly reaction pathways can be specified abstractly in the form of a reaction graph, representing a program to be executed by molecules such as, for example, nucleic acid molecules. A reaction graph provides a simple representation of assembly (and disassembly) pathways that can be translated directly into molecular executables: nodes represent hairpin monomers, ports represent domains, states describe accessibility, arrows represent assembly and disassembly reactions between complementary ports. For example, the reactions depicted in the secondary structure mechanism of FIG. 1 b are specified using a reaction graph in FIG. 1 d. Conventions for the reaction graphs disclosed herein are provided above.

The initial conditions for the program are described via the state of each port in a reaction graph. For example, FIG. 1 e depicts the execution of this reaction graph through cascaded assembly and disassembly reactions. An assembly reaction is executed when ports connected by a solid arrow are simultaneously accessible. For example, for the initial conditions depicted in FIG. 1 d, the program starts with the execution of reaction (1). Reaction 1 (assembly): In an assembly reaction (executed here by the accessible output port of I and the complementary accessible input port of A), a bond is made between the ports and they are flipped, or switched, to inaccessible states; the two output ports of A are flipped to accessible states (based on the internal logic of node A). Reaction 2 (assembly): A bond is made between the newly accessible blue output port of A and the complementary accessible input port of B and both ports are flipped to inaccessible states; the output port of B is flipped to the accessible state (based on the internal logic of node B). Reaction 3 (disassembly): In a disassembly reaction (executed here by the newly accessible output port of B, the inaccessible input port of A, and the inaccessible output port of I), the bond between the output port of I and the input port of A is displaced by a bond between the output port of B and the input port of A; the states of the two output ports are flipped. FIG. 1 f summarizes the hierarchical design process starting from a conceptual dynamic function, a molecular implementation can be realized in three steps: (1) pathway specification via a reaction graph; (2) translation into secondary structure hairpin monomers; (3) computational design of hairpin monomer primary sequences.

Examples of reactions graphs are provided below and include reaction graphs for various dynamic functions, including: catalytic geometry, catalytic circuitry, nucleated dendritic growth and autonomous locomotion.

Monomers

In some embodiments, the reaction graph can be used as a basis for modeling and designing a secondary structure mechanism using hairpin monomers. The reaction pathways by which self-assembly reactions occur are programmed within the primary sequences of the hairpin monomers.

A monomer having the hairpin motif (i.e., “hairpin monomers”) typically has a hairpin structure having at least two distinct, concatenated domains. Typically, a hairpin monomer has at least one input domain and at least one output domain. In preferred embodiments, each domain comprises a nucleation site called a toehold and a propagation region. Preferably, the toehold of a first input domain is exposed and thus available to hybridize to a complementary nucleic acid of another molecule. Preferably, the propagation region of the second domain comprises at least a portion of a hairpin loop region of the hairpin monomer. In preferred embodiments, the toehold of the second domain is hybridized to a portion of the propagation region of the first domain and therefore sequestered in the duplex stem of the hairpin and unavailable to hybridize to a complementary nucleic acid of another molecule. Displacement of the propagation region of the first domain from the toehold of the second domain exposes the toehold such that is becomes available to hybridize with a complementary nucleic acid sequence of another nucleic acid, typically another monomer.

For example, in FIG. 1 a, the monomer A comprises three concatenated domains, a, b and c. In FIG. 1 a, domain a is an input domain, and domains b and c are output domains. In typical embodiments, a hairpin monomer comprises at least two distinct, concatenated domains. In some embodiments, a monomer can comprise two, three, four, five, six or more concatenated domains. Typically, a hairpin monomer has at least one input domain. In some embodiments, a hairpin monomer can have one, two, three, four, five, six or more input domains. In some embodiments in a hairpin monomer having more than one input domain, a first input domain toehold is exposed, and additional input domain toeholds are sequestered. In some embodiments, the sequestered input domain toeholds are sequestered by the duplex stem of the hairpin, and the corresponding domain propagation regions are located on bulge loops. Typically, a hairpin monomer can have one or two output domains. In some embodiments, a hairpin monomer can have one, two, three, four, five, six or more output domains. Typically, the toehold of an output domain is hybridized to a portion of a propagation region of an input domain and therefore sequestered. Displacement of the propagation region of the input domain from the toehold exposes the toehold such that is becomes available to hybridize with a complementary nucleic acid sequence of, generally, another monomer. In some embodiments, the hairpin monomer can have a second output domain. In some embodiments, the second output domain can comprise a single stranded region at an end of a hairpin monomer. For example, the second output domain can have a toehold which is hybridized to a portion of a propagation region of an input domain, and a single stranded propagation region.

Two or more distinct species of hairpin monomers are preferably utilized in a self-assembly pathway. Each monomer species typically comprises at least one domain that is complementary to a domain of another monomer species. However, the monomers are designed such that they are kinetically trapped and the system is unable to equilibrate in the absence of an initiator molecule that can disrupt the secondary structure of one of the monomers. Thus, the monomers are unable to polymerize in the absence of the initiator. Introduction of an initiator species triggers a self-assembly pathway resulting in formation of one or polymers. In some embodiments the polymer comprises only a first and second monomer species. In some embodiments, the polymers can comprise additional nucleic acids. In the examples below, two or more hairpin monomers polymerize in the presence of an initiator to begin a self-assembly pathway. The self-assembly pathways disclosed herein are discussed in more detail below and include, for example, pathways for: catalytic geometry, catalytic circuitry, nucleated dendritic growth and autonomous locomotion. The self-assembly pathways typically result in formation of a polymer, such as, for example, a branched junction, an autocatalytic duplex, a binary molecular tree, or a bipedal walker.

A number of criteria can be used to design the monomers to achieve the desired properties. These include, for example and without limitation, sequence symmetry minimization, the probability of adopting the initiator secondary structure at equilibrium, the average number of incorrect nucleotides at equilibrium relative to the target structure, hybridization kinetics, and the silencing target sequence. The composition of the monomers is not limited to any particular sequences or number of bases, and is designed based on the particular dynamic function. In some embodiments, the composition of the monomers can be designed based on the reaction graph and corresponding secondary structure mechanism of a particular dynamic function

Monomers can be synthesized using standard methods, including commercially available nucleic acid synthesizers or obtained from commercial sources such as Integrated DNA Technologies (Coralville, Iowa). In some embodiments, the monomers can be DNA monomers. In some embodiments, the monomers can be RNA monomers. In some embodiments, the monomers can be RNA-DNA hybrids.

In some embodiments, at least two hairpin monomer species are utilized in a self-assembly pathway as illustrated in FIG. 1 b. In the depicted embodiment, the monomers are denoted A and B. In FIG. 1 b, monomer A comprises three concatenated domains: a, b and c, and monomer B comprises two concatenated domains, represented by b* and c*. Each domain comprises a toehold and a propagation region. In FIGS. 1 a and b, each domain comprises a single sequence segment; however, a domain can comprise any number of sequence segments. In some embodiments, a domain can comprise a portion of a sequence segment. In FIGS. 1 a and 1 b, the small letters with a subscript t denote the toehold of the domain. For example in FIG. 1 a, a_(t) denotes the toehold of domain a. In some embodiments, a toehold can comprise one or more sequence segments, or a portion of a sequence segment. For the example shown in FIG. 1 b, the portion of a domain that is not the toehold is referred to as the “propagation region.” In FIG. 1 b, the small letters represent sequence segments, and letters marked with an asterisk (*) are complementary to the corresponding unmarked letter.

In preferred embodiments, the first stem region of a monomer can hybridize to the second stem region of the monomer to form the hairpin structure. In some embodiments, in the absence of an initiator, the first and second stem regions of each monomer are generally hybridized to form a duplex region of the monomer. The monomers each preferably comprise a hairpin loop region and two “stems regions”—a first stem region and a second stem region that are complementary and together can form a duplex region.

In the embodiment depicted in FIG. 1 b, an initiator I comprises an output domain comprising a* having an exposed toehold a_(t)*. In the depicted embodiment, a first hairpin monomer A comprises an “initiator binding domain” (input domain a having an exposed toehold a_(t)) and a first “assembly domain” (output domain b having a sequestered toehold b_(t)). In the depicted embodiment, a second hairpin monomer B comprises a first “assembly complement domain” (input domain b* having an exposed toehold b_(t)* and a “disassembly domain” (output domain a* having a sequestered toehold a_(t)*).

Assembly according to some embodiments of a self-assembly pathway having catalytic geometry is depicted in FIG. 1 b (1) and (2). A domain a* of the initiator I and the initiator binding domain a of the first hairpin monomer A are typically substantially complementary. That is, the domain a* of the initiator I is able to hybridize to the initiator binding domain a of the first hairpin monomer A, here a portion of domain a.

The initiator preferably comprises an exposed toehold. In FIG. 1 b, the initiator I comprises an exposed toehold a_(t)*, which is a portion of the domain a*. Exposed toehold a_(t)* of the initiator is complementary to a domain a of a first hairpin monomer A. In some embodiments, the initiator binding domain of a first hairpin monomer can comprise an exposed toehold and at least a portion of the first stem region of the first hairpin monomer. For example, in the depicted figure, the first hairpin monomer A has an initiator binding domain a comprising the exposed toehold a_(t) and a portion of the first stem region of A.

Preferably, upon hybridization of the initiator to the exposed toehold of the initiator binding domain of the first hairpin monomer, the second stem region is displaced from the first stem region. This opens the hairpin of the first hairpin monomer. For example, in FIG. 1 b at (1), the initiator I nucleates at the exposed toehold a_(t)* of the first hairpin monomer A by pairing a_(t)* with a_(t). This induces a strand displacement interaction resulting in the hybridization of the initiator I at domain a* to the initiator binding domain a of the first hairpin monomer A to form the first complex (I•A).

In FIG. 1 b, the first complex (I•A) has a newly exposed single-stranded tail that comprises the assembly domain b of the first hairpin monomer A. Monomer A also has another domain, domain c having toehold c_(t), which is newly exposed. The assembly domain b has a newly exposed toehold b_(t).

In some embodiments, the assembly domain of a first hairpin monomer in the first complex can comprise a portion of the loop region and a portion of the second stem region of the first hairpin monomer. For example, in FIG. 1 b, the assembly domain b of first hairpin monomer A comprises a portion of the loop region (the “propagation region” of b) and a portion of the second stem region of A (the toehold b_(t)). In the absence of an initiator, the first and second stem regions of the first hairpin monomer are generally hybridized to form a duplex domain of the first hairpin monomer, and the first assembly domain of the first hairpin monomer is generally not available for hybridization to another monomer.

Preferably, upon hybridization of a newly-exposed toehold of the assembly domain of the first hairpin monomer to the exposed toehold of the assembly complement domain of the second hairpin monomer, the second stem region is displaced from the first stem region. This opens the hairpin of the second hairpin monomer. For example, in FIG. 1 b, the exposed toehold b_(t) of first hairpin monomer A in the first complex I•A nucleates at the exposed toehold b_(t)* of the second hairpin monomer B by pairing segment b_(t) with b_(t)*(FIG. 1 b at (2)). This induces a strand displacement interaction resulting in the hybridization of the first hairpin monomer A at the assembly domain b to the assembly complement domain b* of the second hairpin monomer B to form a second complex (I•A•B). In preferred embodiments, the exposed toehold of assembly complement domain of the second monomer is configured to nucleate at the newly exposed toehold of the assembly domain of the first monomer and not at the propagation region of the assembly domain of the first monomer. Preferably, the assembly complement domain of the second monomer the exposed toehold of assembly complement domain of the second monomer nucleates at the newly exposed toehold, thereby inducing a strand displacement interaction resulting in the hybridization of the assembly domain to the assembly complement domain.

In FIG. 1 b, the second complex (I•A•B) has a newly exposed single-stranded tail that comprises the disassembly domain comprising the segment a* of the second hairpin monomer B.

In some embodiments, the disassembly domain of a second hairpin monomer can comprise a portion of the loop region and a portion of the second stem region of the third hairpin monomer. For example, in the depicted embodiment, the disassembly domain a* of second hairpin monomer B comprises the loop region and a portion of the second stem region of B. In the absence of an exposed second assembly domain, the first and second stem regions of the second hairpin monomer are generally hybridized to form a duplex domain of the second hairpin monomer, and the disassembly domain of the second hairpin monomer is generally not available for hybridization to another monomer.

In some embodiments, instead of a disassembly domain, the second monomer can have a second assembly domain complementary to a second assembly complement domain of a third hairpin monomer. Any number of additional hairpin monomer species having one or more assembly domains can be used in a self-assembly pathway depending on the dynamic function.

In some embodiments, disassembly of an initiator from a monomer or polymer can occur. In some embodiments, polymers can disassemble from polymers, and monomers can disassemble from polymers. For example, disassembly of an initiator from a polymer can occur as generally depicted in FIG. 1 b (3). The second hairpin monomer can have a disassembly domain which is substantially complementary to the initiator binding domain of the first hairpin monomer. In the depicted embodiment, the disassembly domain of the second substrate monomer B comprises a segment a* that is complementary to initiator binding domain a of the first hairpin monomer of the first complex. The disassembly domain a* becomes accessible upon binding of the first assembly domain to the second hairpin monomer and opening of the hairpin of the second hairpin monomer (FIG. 1 b (2)). Preferably, upon hybridization of a newly-exposed disassembly domain to the initiator binding domain of the first hairpin monomer, the initiator is displaced from the first hairpin monomer.

The system illustrated in FIGS. 1 a-f and discussed above exhibits linear growth in response to initiator. However, in some embodiments, monomers can be designed to undergo triggered self-assembly into branched structures exhibiting quadratic growth or dendritic structures exhibiting exponential growth. See, Pierce et al., U.S. patent application Ser. No. 11/371,346, which is herein incorporated by reference in its entirety. In some embodiments, monomers can be designed to undergo autonomous locomotion of a bipedal walker, or other dynamic functions

Exponential growth is limited by the available space such that it decreases to cubic amplification as the volume around the initiator fills. However, if chain reactions products are able to dissociate, exponential growth can be maintained until the supply of monomers is exhausted. In some embodiments, increasing the rate of polymer growth can enhance the ability to, for example detect the presence of low copy number target initiators, such as a single target molecule in a large test volume.

In some embodiments, the secondary structure is preferably such that the monomers are metastable under the reaction conditions in the absence of an initiator. In the presence of an initiator, the secondary structure of a first monomer changes such that it is able to hybridize to an exposed toehold of a second monomer species. This in turn leads to a change in the secondary structure of the second monomer, which is then able to continue the self-assembly pathway to form the desired structure.

Sequence segments of domains (for example, a, b, c, d, q, r, s, t, u, v, x, y and z as illustrated herein) are not limited to any particular sequences or number of bases, and are designed based on the particular dynamic function. In some embodiments, the primary sequence of the monomers can be designed based on the corresponding reaction graph and secondary structure mechanisms.

The length of the toeholds, propagation regions, hairpin loop regions, and stem regions of the monomers can be adjusted, for example to ensure kinetic stability in particular reaction conditions and to adjust the rate of polymerization in the presence of initiator. The hairpin loop regions are preferably between about 1 and about 100 nucleotides, more preferably between about 3 and about 30 nucleotides and even more preferably between about 4 and about 7 nucleotides. In some embodiment the hairpin loop regions of a pair of hairpin monomers can be about 6 nucleotides in length and the stems are about 18 nucleotides long.

The toeholds can be located at any site on a hairpin monomer. The length of the toeholds can be adjusted, for example to ensure kinetic stability in particular reaction conditions and to adjust the rate of polymerization in the presence of initiator. The toeholds are preferably between about 1 and about 100 nucleotides, more preferably between about 3 and about 30 nucleotides and even more preferably between about 4 and about 7 nucleotides. In some embodiment the toeholds of a pair of hairpin monomers can be about 6 nucleotides in length and the stems are about 18 nucleotides long.

Several methods are available to reduce spurious monomer polymerization in the absence of initiator for dynamic functions including those with both higher order growth schemes and linear growth schemes. These include helix clamping, helix lengthening and loop entropy ratchets. In helix clamping, the single stranded regions in one or more of the monomers are truncated at each end so that the helixes that they could potentially invade in other monomers are effectively clamped at the ends by bases that are not present in the single stranded regions. Experiments have shown that this can eliminate any spurious initiation. The amount of truncation that is effective to decrease or eliminate spurious initiation can be determined by routine experimentation. For example, control experiments can be performed using fluorescent gel electrophoresis time courses to monitor strand exchange between single stranded DNA and duplex DNA for different clamp lengths. Using spectrally distinct dyes for the initially single stranded DNA and for the two DNA species in the duplex allows independent monitoring of all species as strand exchange proceeds. These controls can provide a systematic basis for section of clamp dimensions.

In some embodiments utilizing hairpin monomers, loop entropy ratchets are used to reduce self-assembly in the absence of initiator. For example, in some embodiments, an initiator can open a hairpin monomer via a three-way branch migration. This reaction is reversible because the displaced strand is tethered in the proximity of the new helix. However, by increasing the length of the single-stranded loop, the entropy penalty associated with closing the loop increases. As a result, a longer loop will bias the reaction to proceed forward rather than returning to the uninitiated state. However, larger loops are more susceptible to strand invasion. To counter this effect and allow the use of larger loops, mismatches can be introduced between the loop sequences and the complementary regions of the other monomers. Again, the loop length and amount of mismatch that produces the desired reduction in non-specific self-assembly can be determined by the skilled artisan through routine experimentation.

Other refinements to the system stabilize the hairpin monomers to help prevent self-assembly in the absence of an initiator. This can be achieved, for example, via super-stable hairpin loop sequences (Nakano et al. Biochemistry 41:14281-14292 (2002), herein incorporated by reference in its entirety), with ostensible structural features that could further inhibit direct hybridization to the hairpin. In some embodiments, padding segments can be incorporated into the monomer to modulate the lengths of a hairpin monomer's sticky-end, stem, and loop regions, permitting more flexible dimensioning. In some embodiments hairpin loops are made to be self-complementary at their ends. This self-complementation “pinches” the hairpin loops, making them shorter. However, if the reactive exposed toeholds of each monomer are complementary to the hairpin loop regions on the opposite monomer, they will have a slight propensity to close up, thereby slowing down the reaction. This feature can be utilized if a slower reaction is desired. Completely self-complementary hairpins can also be used, for example if the monomer hairpins are forming dimers with interior loops that are more easily invaded than their hairpin counterparts.

In some embodiments, monomers can be derivatized with a compound or molecule, for example, to increase the molecular weight of the polymer resulting from execution of a self-assembly pathway. In some embodiments they can be derivatized at a location that does not interfere with their ability to hybridize. In some embodiments, the monomers comprise a protein-binding region, or other recognition molecule. In some embodiments, the monomers can contain a fluorophore, luminescent molecule, colorimetric compound or other component that allows the resulting polymers and/or the dynamic function to be visualized.

Reaction conditions are preferably selected such that hybridization is able to occur, including between the initiator and the exposed toehold of a first hairpin monomer, between the assembly domain of a first hairpin monomer and an available toehold of a second hairpin monomer, and between the disassembly domain of a second hairpin monomer and the initiator binding domain, between the first and second stem regions of the monomers themselves. At each step of monomer polymerization, energy is gained from the hybridization of the exposed toehold of the monomer. The reaction temperature does not need to be changed to facilitate the polymerization of hairpin monomers. That is, hairpin monomer polymerization or assembly or disassembly reactions are isothermic. They also do not require the presence of any enzymes.

Initiators

As discussed above, an initiator can be a molecule that is able to initiate the polymerization of monomers. Typically, an initiator comprises an output domain that is complementary to an initiator binding domain (which is an input domain) of a hairpin monomer. In some embodiments, a self-assembly pathway is initiated when an initiator interacts with an initiator binding domain of a hairpin monomer, which subsequently undergoes a change in secondary structure, leading to polymer formation. In some embodiments, an initiator can initiate formation of a branched junction, an autocatalytic duplex, a binary molecular tree, or a bipedal walker.

Initiators can be synthesized using standard methods, including commercially available nucleic acid synthesizers or obtained from commercial sources such as Integrated DNA Technologies (Coralville, Iowa). Synthesis is discussed in more detail below. In some embodiments, initiators are naturally-occurring molecules. In some embodiments, initiators could be already present in a system. For example, the initiator can comprise nucleic acid naturally present in a system. In such as system the polymerization of monomers can be used to detect the presence of an initiator.

In some embodiments, the initiator binding domain of a first hairpin monomer is preferably at least 80%, more preferably at least 90%, 95% or higher, complementary to at least a portion of an initiator. In preferred embodiments, the initiator binding domain is at least 2, 3, 4, 5, or 10 or more bases in length.

The initiator preferably comprises a nucleic acid or other molecule that is able to contact a hairpin monomer and initiate a self-assembly pathway. In some embodiments, the initiator comprises a toehold having a sequence that is complementary to a portion, such as, for example without limitation, an exposed toehold, of a monomer, that is available for hybridization with the initiator while the monomer is in its kinetically stable state. In some embodiments, the initiator also preferably comprises a sequence that is complementary to a portion of the monomer adjacent to the toehold such that hybridization of the monomer to the toehold causes a conformational change in the monomer. For example, as depicted in FIG. 1 b, the initiator I can comprise a toehold a* complementary to the initiator binding domain a of a monomer A, where the initiator binding domain a comprises a toehold a_(t) and a portion of a first stem region of the monomer adjacent to the toehold.

In various embodiments, an initiator can be, for example without limitation, an RNA molecule, such as a coding region of RNA, a non-coding region of RNA, a portion of an mRNA, or a microRNA. In some embodiments, an initiator can be, for example without limitation, a DNA molecule such as, for example, a coding strand of DNA, or an antisense DNA.

In some embodiments, the initiator binding domain of a hairpin monomer can be a recognition molecule that specifically binds an initiator molecule. When the initiator interacts with the recognition molecule, the hairpin monomer undergoes a conformational change and the self-assembly pathway is initiated.

Recognition molecules include, without limitation, polypeptides, antibodies and antibody fragments, nucleic acids, aptamers, and small molecules.

In some embodiments, an initiator is bound to an aptamer. In some embodiments, the aptamer-bound initiator is triggerable, such that binding of the aptamer to an appropriate target molecule makes the initiator available to interact with a first hairpin monomer. For example, the initiator binding domain of a first hairpin monomer can bind to an initiator which is bound to an aptamer specific for a target of interest.

Self-Assembly Pathways

Self-assembly pathways for a variety of different dynamic functions can be programmed via reaction graphs. The system illustrated in FIG. 1 a-f and discussed above exhibits linear growth in response to initiator. However, a variety of different dynamic functions can be programmed using the methods disclosed herein. The programming of five different exemplary dynamic functions are generally described below: (1) catalytic formation of branched junctions, (2) autocatalytic duplex formation by a cross-catalytic circuit, (3) nucleated dendritic growth of a binary molecular tree, (4) autonomous locomotion of a bipedal walker, and (5) formation of desired two-dimensional and three-dimensional structures with fluorescent or other identifiable signature characteristics.

Catalytic Geometry

In some embodiments, the self-assembly pathway can be a pathway for catalytic formation of branched junctions. In some embodiments, a branched junction is formed in the presence of an initiator. The initiator can be, for example, any molecule in whose presence formation of a branch junction is desired. Initiators include, without limitation, polypeptides, such as antibodies and antibody fragments, nucleic acids, aptamers, and small molecules.

Compositions and methods are provided for catalyzing the formation of branched junctions. In some embodiments, the branched junction is a 3-arm, 4-arm or k-arm DNA junction (k≧3). For example, 3-arm DNA junctions are illustrated in Example 2, 4-arm DNA junctions are illustrated in Example 4, and k-arm junctions are illustrated in Example 6. The assembly and disassembly pathways for catalytic formation of a 3-arm DNA junction specified in the reaction graph of FIG. 2 a are translated into the motif-based molecular implementation of FIG. 2 b. The complementarity relationships between the segments of hairpins A, B, and C are specified (FIG. 2 b, top) such that in the absence of initiator I, the hairpins are kinetically impeded from forming the three-arm junction that is predicted to dominate at equilibrium. In the reaction graph, this property is programmed by the absence of a starting point if node I is removed from the graph (i.e., no pair of accessible ports connected by an assembly arrow). The introduction of I into the system (FIG. 2 b, bottom) activates a cascade of assembly steps with A, B, and C, followed by a disassembly step in which C displaces I from the complex, freeing I to catalyze the self-assembly of additional branched junctions. The design procedure for the catalytic 3-arm junction system shown in FIGS. 2 a and b is described in detail below in the Examples section.

Each letter-labeled sequence segment shown in FIG. 2 b is six nucleotides in length. However, as discussed above, sequence segments are generally not limited to any particular sequences or number of bases, and are designed based on the particular dynamic function. In FIG. 2 b, the initially accessible toehold (a* for step (1)) or newly exposed toehold (b* for step (2); c* for step (3)) that mediates assembly reactions are labeled with purple letters.

In some embodiments, at least three hairpin monomers are utilized as illustrated in FIG. 2 b to form a 3-arm junction. In FIG. 2 b, the monomers are denoted A, B and C. The monomers each preferably comprise an exposed toehold (for example, toeholds having sequences a, b and c of A, B and C, respectively), a hairpin loop region at the opposite end of the exposed toehold, and two “stems regions,” a first stem region and a second stem region, that together can form a duplex region. The small letters represent sequence segments. Letters marked with an asterisk (*) are complementary to the corresponding unmarked letter.

In preferred embodiments, the first stem region of a monomer can hybridize to the second stem region of the monomer to form the hairpin structure. For example, as shown in FIG. 2 b, the monomer A comprises a first stem region comprising a sequence (x-b-y) that is able to hybridize to the second stem region (y*-b*-x*). In some embodiments, in the absence of an initiator, the first and second stem regions of each monomer are generally hybridized to form a duplex region of the monomer.

In the embodiment depicted in FIG. 2 b, an initiator I comprises a domain comprising the sequence a*-x*-b*-y*. In the depicted embodiment, a first hairpin monomer A comprises an “initiator binding domain” (comprising the sequence a-x-b-y) and a first “assembly domain” (comprising the sequence z*-c*-y*-b*). Typically, the initiator binding domain is an input domain and the assembly domain is an output domain. In the depicted embodiment, a second hairpin monomer B comprises a first “assembly complement domain” (comprising the sequence b-y-c-z) and a second “assembly domain” (comprising the sequence x*-a*-z*-c*). In the depicted embodiment, a third hairpin monomer C comprises a second “assembly complement domain” (comprising the sequence c-z-a-x) and a “disassembly domain” (comprising the sequence y*-b*-x*-a*). In the depicted embodiment, the assembly and disassembly domains are output domains, and assembly complement domains are input domains.

Assembly according to some embodiments of a self-assembly pathway having catalytic geometry is depicted in FIG. 2 b (1)-(3). An output domain (a*-x*-b*-y*) of the initiator I and the initiator binding domain (a-x-b-y) of the first hairpin monomer A are typically substantially complementary. That is, the domain (a*-x*-b*-y*) of the initiator I is able to hybridize to the initiator binding domain (a-x-b-y) of the first hairpin monomer A.

The initiator I preferably comprises an exposed toehold a*, which is a portion of the domain comprising the sequence a-x-b). Exposed toehold a* of the initiator is complementary to a sequence segment a of a first hairpin monomer A. In some embodiments, the initiator binding domain of a first hairpin monomer can comprise an exposed toehold and a portion of the first stem region of the initiator. For example in FIG. 2 b, the first hairpin monomer A has an initiator binding domain a-x-b-y, where a is an exposed toehold, and x-b-y is portion of the first stem region of the first hairpin monomer A.

Preferably, upon hybridization of the initiator to the exposed toehold of the initiator binding domain of the first hairpin monomer, the second stem region is displaced from the first stem region. This opens the hairpin of the first hairpin monomer. For example in FIG. 2 b, the initiator I nucleates at the exposed toehold a of the first hairpin monomer A by pairing segment a* with a (FIG. 2 b at (1)). This induces a strand displacement interaction resulting in the hybridization of the initiator I at a domain a*-x*-b*-y* to the initiator binding domain a-x-b-y of the first hairpin monomer A to form the first complex (I•A).

In some embodiments, the first complex can have a newly exposed single-stranded tail that comprises a first assembly domain of the first hairpin monomer. For example, in FIG. 2 b the first complex (I•A) has a newly exposed single-stranded tail that comprises the first assembly domain (comprising the sequence z*-c*-y*-b*) of the first hairpin monomer A. This first assembly domain has a newly exposed toehold (b*).

In some embodiments, the first assembly domain of a first hairpin monomer in the first complex can comprise a portion of the loop region and a portion of the second stem region of the first hairpin monomer. For example, in FIG. 2 b, the first assembly domain of first hairpin monomer A comprises the sequence z*-c*-y*-b*, where z*-c* is a portion of the loop region and y*-b* is a portion of the second stem region of the first hairpin monomer A. In the absence of an initiator, the first and second stem regions of the first hairpin monomer are generally hybridized to form a duplex domain of the first hairpin monomer, and the first assembly domain of the first hairpin monomer is generally not available for hybridization to another monomer.

Preferably, upon hybridization of a newly-exposed toehold of the first assembly domain of the first hairpin monomer to the exposed toehold of the first assembly complement domain of the second hairpin monomer, the second stem region is displaced from the first stem region. This opens the hairpin of the second hairpin monomer. In the depicted embodiment, the exposed toehold b* of first hairpin monomer A in the first complex I•A nucleates at the exposed toehold b of the second hairpin monomer B by pairing segment b* with b (FIG. 2 b at (2)). This induces a strand displacement interaction resulting in the hybridization of the first hairpin monomer A at the first assembly domain z*-c*-y*-b* to the first assembly complement domain b-y-c-z of the second hairpin monomer B to form a second complex (I•A•B).

In the depicted embodiment, the second complex (I•A•B) has a newly exposed single-stranded tail that comprises the second assembly domain (comprising the sequence x*-a*-z*-c*) of the second hairpin monomer B. This second assembly domain has a newly exposed toehold (c*).

In some embodiments, the second assembly domain of a second hairpin monomer can comprise a portion of the loop region and a portion of the second stem region of the second hairpin monomer. For example, in FIG. 2 b, the second assembly domain of second hairpin monomer B comprises the sequence x*-a*-z*-c*, where x*-a* is a portion of the loop region and z*-c* is a portion of the second stem region of the second hairpin monomer In the absence of an exposed first assembly domain, the first and second stem regions of the second hairpin monomer are generally hybridized to form a duplex domain of the second hairpin monomer, and the second assembly domain of the second hairpin monomer is generally not available for hybridization to another monomer.

Preferably, upon hybridization of a newly-exposed toehold of the second assembly domain of the second hairpin monomer to the exposed toehold of the second assembly complement domain of the third hairpin monomer, the second stem region is displaced from the first stem region. This opens the hairpin of the third hairpin monomer. For example, in FIG. 2 b the exposed toehold c* of second hairpin monomer B in the second complex I•A•B nucleates at the exposed toehold c of the third hairpin monomer C by pairing segment c* with c (FIG. 2 b at (3)). This induces a strand displacement interaction resulting in the hybridization of the second hairpin monomer B at the second assembly domain x*-a*-z*-c* to the second assembly complement domain c-z-a-x of the third hairpin monomer C to form a third complex (I•A•B•C).

In FIG. 2 b the third complex (I•A•B•C) has a newly exposed single-stranded tail that comprises the disassembly domain (comprising the sequence y*-b*-x*-a*) of the third hairpin monomer C. In some embodiments, the disassembly domain of the third hairpin monomer is complementary to a portion of the inhibitor binding domain of the first hairpin monomer.

In some embodiments, the disassembly domain of a third hairpin monomer can comprise a portion of the loop region and a portion of the second stem region of the third hairpin monomer. For example, in the depicted embodiment, the disassembly domain of third hairpin monomer C comprises the sequence y*-b*-x*-a* where y*-b* is a portion of the loop region and x*-a* is a portion of the second stem region of the third hairpin monomer. In the absence of an exposed second assembly domain, the first and second stem regions of the third hairpin monomer are generally hybridized to form a duplex domain of the third hairpin monomer, and the disassembly domain of the third hairpin monomer is generally not available for hybridization to another monomer.

In some embodiments for producing branched junctions with greater than 3 arms, instead of a disassembly domain, the third self-assembly has a third assembly domain complementary to a third assembly complement domain of a fourth hairpin monomer. For the formation of 3-arm branched junctions, preferably three hairpin monomers are used. For the formation of 4-arm branched junctions, preferably four hairpin monomers are used. For the formation of k-arm branched junctions (where k≧3), preferably k hairpin monomers are used. In some embodiments, the kth hairpin monomer can comprise a disassembly domain instead of a kth assembly domain.

In some embodiments, the disassembly domain of the kth hairpin monomer is exposed by the opening of the hairpin of the kth hairpin monomer. The kth hairpin monomer has a disassembly domain which is substantially complementary to the initiator binding domain of the first hairpin monomer. The exposed disassembly domain can bind the initiator binding domain of the first hairpin monomer, thereby displacing the initiator from the kth complex such that the initiator can be recycled to react with another first hairpin monomer.

Disassembly according to some embodiments of a self-assembly pathway having catalytic geometry is depicted in FIG. 2 b (4). The third hairpin monomer C has a disassembly domain which is substantially complementary to the initiator binding domain of the first hairpin monomer A. In the depicted embodiment, the disassembly domain of the third substrate monomer C comprises a sequence y*-b*-x*-a* that is complementary to a sequence of the initiator binding domain a-x-b-y of the first hairpin monomer of the first complex (I•A) that becomes accessible upon binding of the second assembly domain to the third hairpin monomer and opening of the hairpin of the third hairpin monomer (FIG. 2 b (3)). Preferably, upon hybridization of a newly-exposed disassembly domain of the third hairpin monomer to the initiator binding domain of the first hairpin monomer, the initiator is displaced.

In some embodiments, the number of arms of a branch junction depends on the number of hairpin monomer species in the self-assembly pathway. The number and sequences of the hairpin monomers can be designed to provide branched junction having a desired sequence. In some embodiments, the result of the self-assembly pathway can be a 3-arm, 4-arm or k-arm branched junction.

In some embodiments, after displacement by the disassembly domain of the kth hairpin monomer, the displaced initiator can be used in further self-assembly reactions.

In some embodiments, gel electrophoresis can be used to confirm that the hairpins assemble slowly in the absence of initiator and that assembly is dramatically accelerated by the addition of initiator (FIG. 2 c). Disassembly of the initiator enables catalytic turnover as indicated by the nearly complete consumption of hairpins even at substoichiometric initiator concentrations. Lanes 1-4 of the gel in FIG. 2 c show nearly complete conversion of hairpins to reaction products using stoichimetric or substoichiometric initiator I. In some embodiments, only minimal assembly is achieved by annealing the hairpin mixture, illustrating the utility of pathway programming for traversing free energy landscapes with kinetic traps that cannot be overcome by traditional annealing approaches. In FIG. 2 c, minimal conversion is seen in the absence of initiator (lane 5), even with annealing (lane 6).

In some embodiments, direct imaging of the catalyzed self-assembly product (e.g., A•B•C) via atomic force microscopy (AFM) can be used to confirm the expected 3-arm junction morphology as shown in, for example, FIG. 2 d.

In some embodiments, the reaction pathway can be extended to the catalytic self-assembly of k-arm junctions. FIGS. 2 e and f show an example of catalytic self-assembly of a k-arm junction where k=4 in a reaction graph (FIG. 2 e) and AFM image (FIG. 2 f), respectively. A detailed example of the programming for the catalytic formation of a 4-arm junction is provided below in Example 4.

As discussed in more detail below, in some embodiments, the above branched structures can be used to form more elaborate desired and/or predetermined structures, such as two-dimensional structures (closed loop structures) and three-dimensional structures.

Catalytic Circuitry

In some embodiments, the self-assembly pathway can be a pathway for an autocatalytic system with exponential kinetics. Compositions and methods are provided for autocatalytic duplex formation by a cross-catalytic circuit. In some embodiments, the triggered exponential growth of cross-catalytic self-assembly pathway can be used in, for example, engineering enzyme-free isothermal detection methods. In sensing applications, self-replication can provide signal amplification for enzyme-free isothermal alternatives to polymerase chain reaction based on self-assembly reaction pathways.

In some embodiments, programming of the cross-catalytic self-assembly pathways can be executed as shown in FIGS. 3 a and b. The reaction graph of FIG. 3 a generates an autocatalytic system with exponential kinetics. In the corresponding molecular implementation (FIG. 3 b), four hairpin species, A, B, C, and D coexist metastably in the absence of initiator I (FIG. 3 b, top). The initiator catalyzes the assembly of hairpins A and B to form duplex A•B (Steps 1-2, FIG. 3 b, bottom), bringing the system to an exponential amplification stage powered by a cross-catalytic circuit: the duplex A•B has a single-stranded region that catalyzes the assembly of C and D to form C•D (Steps 3-4); C•D in turn has a single-stranded region that is identical to I and can thus catalyze A and B to form A•B (Steps 5-6). Hence, A•B and C•D form an autocatalytic set capable of catalyzing its own production. Disassembly (Steps 2b, 4b, and 6b) is fundamental to the implementation of autocatalysis and sterically uninhibited exponential growth.

In some embodiments, each step in the reaction can be examined using, for example, native polyacrylamide gel electrophoresis to check for the expected assembly and disassembly behavior. System kinetics can be examined via a fluorescence quenching experiment (FIG. 3 c). Spontaneous initiation in the absence of initiator reflects the finite time scale associated with the metastability of the hairpins and yields a sigmoidal time course characteristic of an autocatalytic system. As expected, the curve shifts to the left as the concentration of initiator is increased. A plot of 10% completion time against the logarithm of the concentration exhibits a linear regime, consistent with exponential kinetics and analytical modeling (FIG. 3 c, inset). The minimal leakage of a system containing only A and B (labeled A+B in FIG. 3 c) emphasizes that the sigmoidal kinetics of spontaneous initiation for the full system (A+B+C+D) are due to cross-catalysis.

The cross-catalytic self-assembly pathway demonstrates synthetic biomolecular autocatalysis (see, von Kiedrowski et al., Angew. Chem. Int. Ed. 25, 932-935 (1986); Paul et al., Proc. Natl. Acad. Sci. USA 99, 12733-12740 (2002); Levy, M. & Ellington, A. D., Proc. Natl. Acad. Sci. USA 100, 6416-6421 (2003); Lee et al., Nature 382, 525-528 (1996)) driven purely by the free energy of base-pair formation. Autocatalysis and exponential system kinetics can also be achieved via entropy-driven hybridization mechanisms.

A detailed example of one embodiment for programming catalytic circuitry is provided below in Example 7.

As discussed in more detail below, in some embodiments, the catalytic application can be applied for forming more elaborate desired and/or predetermined structures, such as two-dimensional structures (closed loop structures) and three-dimensional structures, in a catalytic manner. In some embodiments, this can provide for a larger detectable signal (e.g., signature) for the detection of a target.

Nucleated Dendritic Growth

In some embodiments, the self-assembly pathway can be a pathway for nucleated dendritic growth. Compositions and methods for self-assembly pathways are provided in which nucleic acid monomers form dendrimers. In some embodiments, dendrimers are formed only upon detection of a target nucleation molecule. By growing to a prescribed size, such dendrimers can provide quantitative signal amplification with strength exponentially related to in the number of constituent species.

In some embodiments, methods and compositions disclosed herein can be used for in situ amplification in bioimaging applications, such as, for example, in bio-marker generation. The bio-marker can, for example, facilitate fluorescence imaging, molecule sorting, etc. See, Pierce et al., U.S. patent application Ser. No. 11/371,346, which is herein incorporated by reference in its entirety. For example, monomers disclosed herein can be used to self-assemble a fluorescent polymer tethered to a target mRNA to detect expression of the mRNA. In some embodiments, labeled hairpin monomers can self-assemble in the presences of an initiator into a dendrimer of a prescribed size, yielding quantized signal amplification with strength exponential in the number of components. In some embodiments, only the root hairpin monomer and its two child species depend on the sequence of the initiator; thus, the other monomers do not need to be redesigned for each target initiator.

The molecular program in FIG. 4 a depicts the triggered self-assembly of a binary molecular tree of a prescribed size. In the depicted embodiment, the reaction starts with the assembly of an initiator node I with a root node A1. Each assembled node subsequently assembles with two child nodes during the next generation of growth, requiring two new node species per generation. In the absence of steric effects, a G-generation dendrimer uses 2G-1 node species and yields a binary tree containing 2G-1 monomers, i.e., a linear increase in the number of node species yields an exponential increase in the size of the dendrimer product. FIG. 4 b depicts the motif based implementation of the program depicted in FIG. 4 a: Hairpins are metastable in the absence of initiator; the initiator I triggers the growth of a dendrimer with five generations of branching (G5).

In one embodiment, trees with G=1, 2, 3, 4, and 5 are constructed. The nucleated growth of the trees can be examined using, for example, native agarose gel electrophoresis. Band shifting demonstrates increasing dendrimer size with each generation of growth (FIG. 4 c). FIG. 4 d demonstrates that the concentration of dendrimer depends linearly on the concentration of the initiator in the system. Finally, AFM imaging of dendrimers for G=3, 4, and 5 reveals the expected morphologies (FIG. 4 e). Measurements of the dendrimer segment lengths agree well with the design.

A detailed example of one embodiment for programming nucleated dendritic growth is provided below in Example 9.

In some embodiments, the above structures can be used to form more elaborated desired and/or predetermined structures, such as two-dimensional structures (closed loop structures) and three-dimensional structures.

Autonomous Locomotion

In some embodiments, the self-assembly pathway can be a pathway for autonomous locomotion. Compositions and methods are provided for an autonomous enzyme-free bipedal DNA walker capable of stochastic locomotion along a DNA track. In some embodiments, the bipedal DNA walker system can mimic the bipedal motor protein, kinesin, which hauls intracellular cargo by striding along microtubules. Asbury et al., Curr. Opin. Cell Biol. 17, 89-97 (2005).

In some embodiments of a system for autonomous locomotion, they system comprises two species of “fuel” hairpin monomers, and a bipedal walker. In various embodiments, one species of fuel hairpin monomer (“track monomers”) can be linearly arranged at regular intervals along substrate to form a track for a bipedal walker. In some embodiments, the substrate can comprise a nicked DNA duplex. Typically, the track monomers comprise an input domain and an output domain. A bipedal walker comprises two identical “walker legs” connected by a duplex torso (FIG. 5 b). The walker legs comprise an output domain complementary to an input domain of the track monomers. The bipedal walker assembles with the track monomers. In the presence of the second fuel hairpin monomer assembles with a track monomer, which subsequently displaces from the bipedal walker. Typically, a second “fuel” hairpin monomer species comprises an input domain complementary to the output domain of the track monomer species, and an output domain complementary to the input domain of the track monomer species. The bipedal walker moves unidirectionally along the linear track by sequentially catalyzing the formation of a “track monomer-second fuel hairpin monomer” complex.

The molecular program in FIG. 5 a depicts a self-assembly pathway the stochastic movement of a bipedal walker. Joined by a duplex torso, each of two identical walker legs, I, is capable of catalyzing the formation of waste duplex A•B from metastable fuel hairpins A and B via a reaction pathway in which I assembles with A, which assembles with B, which subsequently disassembles I from the complex. FIGS. 5 a and b depict a reaction graph and corresponding molecular implementation for an exemplary bipedal walker. As shown in FIG. 5 b, in some embodiments, the track can consist of five A hairpins arranged linearly at regular intervals along a nicked DNA duplex. In the presence of hairpin B, a sub-population of walkers will move unidirectionally along the track by sequentially catalyzing the formation of A•B. Due to the one-dimensional arrangement of anchor sites, this processive motion occurs only for those walkers that exhibit a foot-over-foot gait by stochastically lifting the back foot at each step.

One embodiment of a fuel system for a walker system is shown in FIG. 30 a. Hairpins A and B in co-exist metastably in the absence of catalyst I. Catalyst I catalyzes A and B to form duplex A•B. Step 1: the toehold a* of I nucleates at the toehold a of A, resulting in the opening of the hairpin A and the formation of the product I•A. Step 2: I•A, with c* newly exposed, opens hairpin B; B subsequently displaces I from A, producing waste product A•B.

In some embodiments, walker locomotion can be investigated using a bulk fluorescence assay that tests whether there is a sub-population of walkers that locomotes processively through positions 3, 4, and 5, starting from an initial condition with legs anchored at positions 1 and 2. Quenchers are attached to the walker's legs and spectrally distinct fluorophores are positioned proximal to anchorages 3, 4, and 5. Consistent with processivity, the anticipated sequential transient quenching of the fluorophores at positions 3, 4, and 5 is observed (FIG. 5 c).

To rule out the possibility that this signal arises from non-processive walker diffusion through the bulk solution from one position to the next, monopedal walkers that lack a mechanism for achieving processivity can be used. In this case, the sequential transient quenching will no longer match the ordering of the fluorophores along the track (FIG. 5 d) and the time scale for visiting any one of the three anchorages is longer than the time scale to visit all three anchorages for the bipedal system (FIG. 5 e).

Additional control experiments show that this difference in time scales cannot be explained by the relative rates with which freely diffusing bipedal and monopedal walkers land on the track. As a further test of processivity for the bipedal walker, reordering the fluorophores along the track leads to the expected change in the ordering of the transient quenching (FIG. 5 f).

A detailed example of one embodiment for programming autonomous locomotion is provided below in Example 11.

In some embodiments, the walkers can be labeled with fluorescent probes and used for detection purposes (e.g., as a barcode).

Pathway Analysis

The hairpin monomers, polymers, self-assembly pathway reactions and dynamic functions can be analyzed by any of a variety of methods known in the art. For example, gel electrophoresis can be used to compare the hairpin monomers before and after the reaction. For example, an amount of each monomer species can be mixed and mixed with varying amounts of initiator and a control (e.g., reaction buffer only). The samples can be allowed to react for a suitable time, such as for example without limitation 2 hours. The annealed can be mixed with loading buffer mix was loaded into a gel. The gel can be run and the nucleic acid visualized under UV light. In some embodiments, the gel can be imaged using an imaging system such as, for example, an FLA-5100 imaging system (Fuji Photo Film Co., Ltd.).

In some embodiments, the hairpin monomers and polymers can be visualized using an atomic force microscope (AFM). For example, images can be obtained using a multimode scanning probe microscope, equipped with an Q-control module for analog AFMs. In some embodiments, samples can be first diluted in an appropriate buffer to achieve the desired sample density. The diluted sample can be applied onto the surface of freshly cleaved mica and allowed to bind. Supplemental Ni⁺⁺ can be added to increase the strength of DNA-mica binding. H. G. Hansma and D. E. Laney, Biophysical Journal, 70:1933-1939, 1996. Before placing the fluid cell on top of the mica puck, an additional amount of buffer can be added to the cavity between the fluid cell and the AFM cantilever chip to avoid bubbles.

In some embodiments, fluorescence data can be obtained by, for example, a spectrofluorometer. For example, excitation and emission wavelengths were set to 394 nm and 517 nm (for FAM), 527 nm and 551 nm (for JOE), and 558 nm and 578 nm (for TAMRA), respectively, with 4 nm bandwidth. The assembly of the walker system is described above. In the experiments, an amount of the track and an amount of the bipedal walker can be used to assemble the system. In some embodiments, a sub-stoichiometric amount of walker can be used to ensure that no free-floating walker would bind to the hairpin monomer on the track. For the same reason, a sub-stoichiometric amount of monopedal walker can be used in the diffusion experiments. The assembled track can be introduced first to record the three fluorescence baselines of FAM, JOE, and TAMRA. The hairpin monomer is then introduced to start the walker's locomotion.

Compositions for Self-Assembly Pathways

Compositions and kits for self-assembly pathways are contemplated for use within the scope of the subject matter. In preferred embodiments, the compositions comprise a first hairpin monomer and a second hairpin monomer. In some embodiments, the compositions comprise a first hairpin monomer, a second hairpin monomer and a third hairpin monomer. In some embodiments, the compositions comprise a first hairpin monomer, a second hairpin monomer, a third hairpin monomer and a fourth hairpin monomer. Additional monomers can be included in some embodiments. In the presence of initiator, a self-assembly pathway is initiated causing the initiation of the desired dynamic function. In some embodiment, the dynamic function results in formation of a polymer. In some embodiments, in the presence of a catalyst, autonomous locomotion is initiated.

The compositions can also contain other components, such as, for example, accessory molecules that facilitate initiator recognition and aid the formation of polymers. Accessory molecules typically comprise nucleic acid molecules. In some embodiments, the accessory molecules are DNA helper strands that bind to regions flanking an initiator nucleic acid sequence. Preferably the accessory molecules are DNA helper strands that bind to regions flanking the binding site on an initiator.

Furthermore, the composition can comprise a carrier that facilitates the introduction of nucleic acids, such as, for example, nucleic acid monomers and accessory nucleic acid molecules, into a cell, such as a cell containing an initiator associated with a disease or disorder. Carriers for delivery of nucleic acids into cells are well known in the art and examples are described above.

In some embodiments, a computer program is provided that designs and/or aids in the design of the primary sequences of hairpin monomers. In some embodiments, a program can be used that specifies assembly and/or disassembly pathways for dynamic functions using nodal abstractions. In some embodiments, the program translates nodal abstractions into hairpin motifs. In some embodiments, the program designs primary sequences of hairpin monomers. In this manner, primary sequences for hairpin monomers for implementing a dynamic pathway can be provided by the program. In some embodiments, the program performs any of the methods described herein. In some embodiments, the computer software used to design the structures can be nupack.org.

Molecular Compilers

Within the nucleic acid design community, it is common practice to specify a design as a set of one or more static target secondary structures. Seeman, Nature 421, 427-431 (2003). The sequences of the constituent strands are then typically designed by optimizing an objective function that captures some combination of affinity and/or specificity for the target structures. Seeman, J. Biomol. Struct. Dyn. 8, 573-581 (1990); Hofacker et al., Chem. Mon. 125, 167-188 (1994); Andronescu et al., J. Mol. Biol. 336, 607-624 (2004); Dirks et al., Nucleic Acids Res. 32, 1392-1403 (2004).

By contrast, dynamic function encoded in a self-assembly system can be designed by programming the reaction pathway of the system as described herein. The intended dynamic function is first specified using a reaction graph. The reaction graph is then implemented in terms of the present hairpin motif, and finally the molecular implementation is encoded in the primary sequences of a set of nucleic acid strands of the hairpin monomers. As such, the standardized hairpin motif and the reaction graph provide layers of abstraction that bridge the description of the dynamic behavior of the system and the set of nucleic acid primary sequences, which implement the target behavior.

In some embodiments, automating the process depicted in the reaction graph can provide a biomolecular compiler that can take the desired dynamic function as input, translate it first to a reaction graph, then to a motif-based molecular implementation, and subsequently into nucleic acid sequences that encode the intended dynamic function.

In some embodiments, a method for preparing hairpin monomers for carrying out a dynamic function is provided. In some embodiments, the method includes: providing an input, switching the state of a first input port on a first nodal abstraction from accessible to inaccessible, switching the state of a first output port on the first nodal abstraction from inaccessible to accessible; switching the state of a second input port on a second nodal abstraction from accessible to inaccessible and switching the state of the first output port on the first nodal abstraction from accessible to in accessible; and designing a first hairpin monomer based on the first nodal abstraction and a second hairpin monomer based on the second nodal abstraction, wherein the first and second hairpin monomers self-assemble in the presence of an initiator to perform the dynamic function. In some embodiments, a step of designing nucleic acid primary sequences for the first hairpin monomer and second hairpin monomer can be included in the method.

Triggered Fluorescent Geometric Barcode

Several embodiments described herein relate to generating fluorescent geometric “barcodes” using self-assembling hairpin monomers. Such fluorescent geometric barcodes can expand the number of unique probes available for use in microscopic imaging. Ultra-high-resolution fluorescence microscopy has achieved spatial resolutions far below the ˜300 nanometer light diffraction limit. For example, using stochastic optical reconstruction microscopy (STORM), researchers have demonstrated 3-color imaging of mammalian cells with ˜25 nm resolution. With this level of resolution, the spatial arrangement of fluorophores in a programmable structure based on triggered molecular geometry can be distinguished as a fluorescent barcode. Such fluorescent barcodes can be used, for example, to differentiate target mRNA species for the simultaneous imaging of a large number of mRNA species.

The use of geometric fluorescent barcode devices is not limited to any particular imaging technology, and is compatible with any imaging technique that achieves appropriate resolution to distinguish a structured arrangement of fluorophores. Examples of super-resolution imaging techniques include stimulated emission depletion microscopy (STED) and the related techniques of ground state depletion (GSD) and saturated structured illumination (SSIM). These techniques are referred to as ensemble focused light imaging techniques, and are based on non-linear optical effects that utilize the application of multiple high-intensity pulsed lasers with specialized modulation filters to control the excitation beam geometry. STED instruments utilize a raster-scan imaging scenario similar to a laser-scanning confocal microscope. Another super-resolution imaging technique, stochastic optical reconstruction microscopy (STORM), by contrast, is a single-molecule approach that relies on activation of a limited subset of the overall molecular population to sequentially image and localize individual emitters on a temporal basis.

One challenge in using fluorescence as an indicator for the presence of various species in a sample is how to detect many distinct species simultaneously, in a common reaction volume. The number of spectrally distinguishable fluorophore labels that can currently be resolved is generally between 3 and 6 species.

Some embodiments provided herein provide how this can be overcome by incorporating the fluorescent molecules into a probe with structured geometry. As generally depicted in FIG. 37, fluorescently labeled hairpin monomers are designed to self-assemble into a rigid structure. In some embodiments, the structure is asymmetric. The number of different targets that can be simultaneously imaged is determined by the formula d^(k), with k representing the differentiable tag positions and d the distinct tags (e.g. fluorophores). For example, if k=5 and d=4, a total number of 1024 distinct molecule species can be imaged simultaneously. One of ordinary skill in the art would understand that for any given asymmetric or 3-dimensional structure, the barcode can be varied by labeling different hairpin monomers or by labeling the hairpin monomers with different fluorophores.

An example of an implementation scheme for a k=4, d=4 barcode is depicted at FIG. 38. In the embodiment shown at FIG. 38 a, fluorophore decorated hairpin monomers co-exist meta-stably in the absence of the target mRNA (T). In the presence of the mRNA target (T), the hairpins are triggered to self-assemble into a tetrahedron.

The embodiment shown at FIG. 38 a, is a non-catalytic version of the triggered formation of a DNA tetrahedron where the tetrahedron stays attached to T. Several embodiments include a catalytic version, where the barcode is released from the target. An advantage of the catalytic scheme is that the signal is amplified such that one copy mRNA target can trigger the formation of many copies of the barcode. An advantage of the non-catalytic scheme is that the barcode stays attached to T, indicating the sub-cellular location of the target mRNA. Both catalytic and non-catalytic embodiments are contemplated herein.

FIG. 38 b depicts an embodiment where the hairpin monomers are labeled with both a fluorophore and a quencher so that the fluorophores are initially quenched in the DNA hairpin configuration, and they only become bright upon the detection of a target mRNA and the subsequent formation of the programmed 3-dimensional structure. In this embodiment background fluorescence is suppressed. Even in the absence of quenching or in cases of incomplete quenching of the fluorophore, the prescribed spatial pattern formed by the fluorophores incorporated into the structure of the barcode allows the organized fluorescent barcode to be distinguished from the random pattern formed by unorganized background fluorophores. In some embodiments, other fluorescence modification approaches can be used apart from simply quenching and/or FRET based approaches.

In some embodiments, part of the probe design employs simple fluorescence and another part of the probe structure employs a FRET based system or other fluorescence modification approach.

While the embodiments shown at FIG. 38 are tetrahedrons, fluorescent barcodes can comprise any structured geometry. In some embodiments, the hairpin monomers can self-assemble into a 2-dimensional structure. An example of a 2-dimensional structure is a binary “tree” based on the nucleated dendritic growth system shown in FIG. 4 a-e. In some embodiments, the hairpin monomers can self-assemble into a 3-dimensional structure. Non-limiting examples of 3-dimensional structures that the hairpin monomers can be programmed to assume include cubes, cuboids, dodecahedrons, octahedrons, pyramids, and tetrahedrons or complex polyhedrons with 6-10,000 edges.

There are a variety of approaches for delivering hairpin monomers to a cell or tissue to be imaged and there is no specific limitation for the methods provided herein. Non-limiting examples of suitable delivery technologies include lipofectamine mediated transfection, retroviral vector, adenoviral vector, nucleofection and microinjection, and other delivery methods known to the field. In some embodiments, the components (or entire structures disclosed herein) can be delivered to a target area and/or tissue and/or cell by a variety of ways. In some embodiments, the material can be delivered to fixed cells and/or cell lysates. In some embodiments, delivery to fixed tissue can be achieved as outlined in Choi et al., “Programmable in situ amplification for multiplexed imaging of mRNA expression,” Nature Biotechnology, 28:1208-1214 (2010). In some embodiments, delivery to fixed cells can be achieved by smFISH, e.g., in the manner described in Zenklusen et al., “Single-RNA counting reveals alternative modes of gene expression in yeast,” Nat. Struct. Mol. Biol., 15:1263-1271 (2008) and Raj et al., “Imaging individual mRNA molecules using multiple singly labeled probes. Nature Methods, 5:877-879 (2008). In some embodiments, delivery to cell lysate can be achieved employing nanostring technology, e.g., as described in Geiss et al., “Direct multiplexed measurement of gene expression with color-coded probe pairs,” Nature Biotechnology, 26: 317-325 (2008). The entireties of each of which is herein incorporated by reference. In some embodiments, these delivery methods can be used for delivery of the triggered fluorescent barcode.

In some embodiments, the components are sufficiently resistant to nuclease digestion. Chemical modifications of the nucleic acid backbones can be incorporated to enhance the stability of the hairpin monomers and the fluorescent barcode. For example, phosphothioate modification of the backbone of RNA significantly increases its nuclease resistance and such modified nucleic acids are commercially available.

In some embodiments, multiple barcode systems can be provided to a cell or tissue. There is no fundamental information or physical limit to the number of barcode systems that may be provided. For example, in a 20 base nucleic acid strand there are 4²⁰≈10¹² or 1 trillion different possible sequences; and the hairpin monomers can be engineered to differentiate a single base mismatch. Probabilistic calculation shows that for barcodes each with a ˜1000 μm³ visual volume (i.e. for a 25 nm resolution microscope), the typical ˜1000 μm³ volume of a eukaryotic cell allows all the barcodes to be sufficiently separated in space and thus be imaged with high probability. Automated design software can be employed to design multiple unique fluorescent barcodes and a large number of monomers can be synthesized in a high throughput and economical fashion. For example, Agilent® DNA microarray printers can synthesize 244,000 distinct DNA strands in parallel.

Triggered Fluorescent Protein Spatial Organizer

Several embodiments described herein relate to triggered geometric organizers for proteins, including fluorescent proteins. Embodiments employing fluorescent proteins allow for a more in vivo or cellular approach in which fluorescent probes need not be added to a tissue or cell sample. Indeed, in some embodiments, the cells themselves can produce the hairpin monomers and/or the fluorescent proteins.

Fluorescent proteins (FPs) are proteins that have a chromophore within their own polypeptide sequence. An application of FP technology is to introduce a gene (or a gene chimera) encoding an engineered fluorescent protein into living cells and subsequently visualize the location and dynamics of the gene product using fluorescence microscopy. The first fluorescent protein discovered was green fluorescent protein (GFP), which has an excitation maximum at 395 nanometers (and a less prevalent, unprotonated form that absorbs at approximately 475 nanometers) and a fluorescence emission maximum peak wavelength at 507 nanometers. A broad range of fluorescent protein genetic variants have been developed that feature fluorescence emission spectral profiles spanning almost the entire visible light spectrum. Examples of other fluorescent proteins include, but are not limited to: enhanced green fluorescent protein (EGFP), Emerald, Superfolder GFP, Azami Green, mWasabi, TagGFP, TurboGFP, AcGFP, ZsGreen, T-Sapphire, blue fluorescent protein (BFP), enhanced fluorescent protein (EBFP), EBFP2, Azurite, mTagBFP, cyan fluorescent protein (CFP), enhanced cyan fluorescent protein (ECFP), Cerulean, CyPet, AmCyan1, Midori-Ishi Cyan, TagCFP, mTFP1 (Teal), yellow fluorescent protein (YFP), enhanced yellow fluorescent protein (YFP), Topaz, Venus, mCitrine, YPet, TagYFP, PhiYFP, ZsYellow1, mBanana, orange fluorescent protein (OFP), Kusabira Orange, Kusabira Orange2, mOrange, dTomato, mTangerine, red fluorescent proteins (RFP), DsRed, mRuby, mApple, mStrawberry, AsRed2, JRed, mCherry, HcRed1, mRaspberry, dKeima-Tandem, HcRed-Tandem, mPlum, and AQ143.

While most small fluorescent molecules, such as fluorescein isothiocyanate (FITC), are strongly phototoxic when illuminated in live cells, fluorescent proteins are usually much less toxic to living cells. This allows for the observation of cells expressing one or more proteins tagged with fluorescent proteins over time. Prior applications of FPs were limited in the following ways: a) to monitor the expression of a target gene, a FP gene must be genetically fused with the target gene, which is tedious, technically challenging, and could affect the natural expression of the target gene; and b) the expressed FP protein was often structurally linked to the target protein, which while enabling sub-cellular spatial tracking of the protein, could interfere with the target protein's native function.

In some embodiments, the triggered molecular geometry described herein can be employed to build a fluorescent protein organizer that dynamically links target gene expression (or the presence of any target molecule) to triggered formation of an imageable spatial arrangement of FPs. In some embodiments, by transducing the molecular event of gene expression to the imageable spatial arrangement of FPs, the geometric organizer avoids the need to genetically fuse the FP gene with the target gene, making FP technology much more flexible, expressive, and easier to use. In some embodiments, the triggered fluorescent protein spatial organizer can be engineered such that the organizer is structurally linked to the target mRNA and/or protein to enable spatial tracking (e.g. as in FIG. 40 b 1). In some embodiments, the triggered fluorescent protein spatial organizer separates from the target mRNA and/or protein to avoid or reduce disruption of their native functions (e.g. as in FIG. 40 b 2-3).

In some embodiments, FPs are fused to a peptide adaptor, which can specifically bind to an RNA or DNA aptamer. In some embodiments, aptamers are engineered through directed in vitro protein evolution to show specific and potent (e.g. pico to nano to micromolar binding affinity) binding to their protein targets. In some embodiments, previously characterized aptamer-peptide pairs can be used, providing many potential candidates for engineering the FP-hairpin complex.

In several embodiments, different FPs are fused to different peptide adaptors, which each binding to a specific aptamer. In some embodiments, the peptide adaptors bind to specific aptamer modified hairpins. In some embodiments, binding of the peptide adaptor to an aptamer modified hairpin triggers self-assembly of the metastable hairpin monomers into a prescribed shape, arranging the conjugated FP proteins into a corresponding geometrical pattern. In some embodiments, the presence of a target (e.g., protein, mRNA, etc.) triggers the self-assembly of FP-conjugated metastable hairpin monomers into a prescribed shape, arranging the conjugated FP proteins into a corresponding geometrical pattern.

Many different implementation schemes for the triggered geometric organizers are contemplated, four of which are depicted in FIGS. 40 b 1-b 4. FIG. 40 b 1 depicts the self-assembly of meta-stable FP-conjugated hairpins into a binary “tree” based on a nucleated dendritic growth system upon being triggered by a target mRNA. In some embodiments, aggregation of the initially dispersed FP-conjugated hairpins can be observed as the appearance of a bright dot using traditional fluorescence microscopy. In some embodiments, the binary tree provides a collection of the same or similar FPs, so that a brighter signal is generated. Thus, in some embodiments, the method provides for same color aggregation of the FPs upon detection of a target.

FIG. 40 b 2 depicts the mRNA target-mediated catalysis of distinctly colored FP-conjugated hairpins to form a trimer based on a catalytic branch formation system. In some embodiments, the assembled FP-conjugated trimers can be visualized using fluorescence correlation spectroscopy. In some embodiments, dimers are formed. In some embodiments tetramers are formed. In some embodiments, any number of species can be aggregated together, e.g., 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, etc. of FPs. In some embodiments, one or more of the FPs in the aggregate has different spectral properties (e.g., emission spectra, excitation spectra, anisotropy, etc.) so as to produce a (relatively) unique signature for the aggregated complex. The term “unique” when used in reference to a signature does not require absolute uniqueness for all embodiments. Rather, the signature should be adequately unique for the purpose for which the aggregate is being used.

FIG. 40 b 3 depicts the self-assembly of FP-labeled hairpins into a four-arm junctions based on a catalytic 4-arm junction formation system. In the embodiment depicted at FIG. 40 b 3, both the 5′ and 3′ ends of a set of hairpin monomers are modified with aptamers that bind to a peptide tag bound to the same color FPs. A cross-structure is formed by 2 FP-conjugated and 2 FP′-conjugated hairpins, such that two distinct color FPs are co-localized on the same end of a DNA duplex arm of the 4-arm junction, resulting in a FRET pair. In some embodiments, the 4-arm junctions can be observed using FRET fluorescence microscopy techniques. In some embodiments, other fluorophore type interactions can be employed (rather than simply FRET). In some embodiments, the number of arms can be varied. In some embodiments, there are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more arms, including any range defined between any two of the preceding values. In some embodiments, the FP can be combined with one or more non-protein fluorophores (and thus aspects such as anisotropy and quenching can be examined of the non-protein fluorophores).

In the embodiments depicted in FIG. 40 b 4, mRNA target catalyzes the formation of a tetrahedron with FP decorated vertices. In some embodiments, the geometric fluorescent protein organizer can be observed using ultra-high resolution microscopy. In some embodiments, the triggered organization of the fluorescent proteins can be monitored via native gel electrophoresis and a fluorescent gel scanner. In some embodiments, the structures involve more than the 4 points of a tetrahedron, for example, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 25, 30, 35, 40, 50 or more points of intersection. In some embodiments, the structures involve more than the 6 legs of a tetrahedron, e.g., 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 27, 32, 37, 42, 52, or more legs.

Triggered Self-Assembly of a Geometric Marker for Electron Cryotomography

Several embodiments described herein relate to visual and/or physical markers for various molecular imaging approaches, such as electron cryotomography based on triggered molecular geometry. Electron cryotomography (ECT) enables imaging of macromolecules, viruses, and even small whole cells, in their nearly native states at nanometer resolution. ECT involves collecting a series of 2-dimensional projections imaged at various angles relative to the incident electron beam. Each of the projection images contains information from all heights of the specimen collapsed into a single plane, which makes it is possible to use weighted back-projection algorithms to reconstruct the 3-dimensional volume of the specimen Present-day implementations of tomography lack visual markers that can uniquely identify target macromolecules.

In some embodiments, the triggered molecular constructs described herein can be employed to label a target with a prescribed 3-dimensional (or two-dimensional) nucleic acid shape when the target is present in a sample. In some embodiments, the electron dense prescribed 3-dimensional (or two-dimensional) nucleic acid shape can be imaged using ECT and thus provides a “visual” marker for ECT. The clarity of ECT images depends upon the electron density of the marker. In some embodiments, clarity is enhanced by engineering a self-assembled nucleic acid structure with a high number of nucleic acid molecules to have a higher electron density. In some embodiments, nucleic acid molecules are incorporated by adding struts to a 3-dimensional marker. In some embodiments, one to ten, ten to twenty, twenty to fifty, fifty to one hundred, one hundred to two hundred, two hundred to five hundred, or five hundred to one thousand nucleic acid struts are incorporated into a 3-dimensional (or two-dimensional) marker.

In some embodiments, a target protein is structurally fused to a peptide tag, which serves as an adaptor for binding to a selected nucleic acid aptamer. Nucleic acid hairpin monomers are triggered by the presence of the aptamer to self-assemble into a prescribed geometric shape attached to the tail of the green aptamer. In some embodiments, the prescribed 3-dimensional shape is a tetrahedron. In some embodiments, the shape can be any of those described herein. In some embodiments, the stoichiometry between the aptamer and the peptide tag are controlled so that there are no excessive unbound aptamers, which could trigger the spurious formation of geometric structures, in the cell.

In several embodiments a “triggerable” aptamer is used. In these embodiments, the triggerable aptamer is triggered into an activated, open configuration upon binding to the peptide adaptor. The hairpin monomers are only triggered to self-assemble a prescribed geometric shape in the presence of the active aptamer.

Exemplary Assembly of Three-Dimensional Structures

Assembly and disassembly pathways for catalytic formation of a exemplary tetrahedron comprising a plurality of 3-arm DNA junctions are illustrated in Example 27. The complementarity relationships between the segments of hairpins A1, A2, A3, B1, B2, B3, C1, C2, and C3 are specified (FIG. 43 a) such that in the absence of initiator T, the hairpins are kinetically impeded from forming the junctions that are predicted to dominate at equilibrium. The introduction of T into the system activates a cascade of assembly steps for A1, A2, and A3, which includes a disassembly step in which A3 displaces T from the complex.

In some embodiments, at least nine hairpin monomers are utilized, as illustrated in FIGS. 43 a-d, to form a tetrahedron. In FIGS. 43 a,-d the monomers are denoted A1, A2, A3, B1, B2, B3, C1, C2, and C3. A1 binds to a target, which exposes a region that is bound by A2, which in turn exposes a region that is bound by A3. A3 then binds to the region of A1 that was initially bound to the target. Opened hairpin A1 then binds and opens hairpin B1, which in turn binds and opens hairpin C1; opened hairpin A2 binds and opens hairpin B2, which in turn binds and opens hairpin C2; and opened hairpin A3 binds and opens hairpin B3, which in turn binds and opens hairpin C3. Finally, opened hairpin C1 binds to opened hairpin B2, opened hairpin C2 binds to opened hairpin B3, and opened hairpin C3 binds to opened hairpin B1.

The monomers in FIG. 43 each preferably comprise an exposed toehold (for example, toeholds having sequences a, c, e, b, d, f, g, i, and k of A1, A2, A3, B1, B2, B3, C1, C2, and C3, respectively), a hairpin loop region at the opposite end of the exposed toehold, and two “stem regions,” a first stem region and a second stem region, that together can form a duplex region. The small letters represent sequence segments. Letters marked with an asterisk (*) are complementary to the corresponding unmarked letter.

In preferred embodiments, the first stem region of a monomer can hybridize to the second stem region of the monomer to form the hairpin structure. For example, as shown in FIG. 43 a, the monomer A1 comprises a first stem region comprising a sequence (b-c-d) that is able to hybridize to the second stem region (b*-c*-d*). In some embodiments, in the absence of an initiator, the first and second stem regions of each monomer are generally hybridized to form a duplex region of the monomer.

In some embodiments, as depicted in FIG. 43 a, an initiator T comprises a domain comprising the sequence a*-b*-c*-d*. In the depicted embodiment, a first hairpin monomer A1 comprises an “initiator binding domain” (comprising the sequence a-b-c-d), a first “assembly domain I” (comprising the sequence f*-e*-d*-c*), and a first “assembly domain II” (comprising the sequence b*-g*-h*). In the depicted embodiment, a second hairpin monomer A2 comprises a first “assembly complement domain” (comprising the sequence c-d-e-f), a second “assembly domain I” (comprising the sequence b*-a*-f*-e*), and a second “assembly domain II” (comprising the sequence d*-i*-j*). In the depicted embodiment, a third hairpin monomer A3 comprises a second “assembly complement domain” (comprising the sequence e-f-a-b), a “disassembly domain” (comprising the sequence d*-c*-b*-a*), and a third “assembly domain II” (comprising the sequence f*-k*-1*).

In the depicted embodiment, a fourth hairpin monomer B1 comprises a third “assembly complement domain” (comprising the sequence b-g-h), a fourth “assembly domain I” (comprising the sequence h*-n*), and a fourth “assembly domain II” (comprising the sequence g*-m*-j). In the depicted embodiment, a fifth hairpin monomer B2 comprises a fourth “assembly complement domain” (comprising the sequence d-i-j), a fifth “assembly domain I” (comprising the sequence q*-j*), and a fifth “assembly domain II” (comprising the sequence i*-p*-l). In the depicted embodiment, a sixth hairpin monomer B3 comprises a fifth “assembly complement domain” (comprising the sequence f-k-l), a sixth “assembly domain I” (comprising the sequence t*-l*), and a sixth “assembly domain II” (comprising the sequence k*-r*-h).

In the depicted embodiment, a seventh hairpin monomer C1 comprises a first “assembly complement domain I” (comprising the sequence g-m-j*) and a first “assembly complement domain II” (comprising the sequence q-j-m*). In the depicted embodiment, an eighth hairpin monomer C2 comprises a second “assembly complement domain I” (comprising the sequence i-p-l*) and a second “assembly complement domain II” (comprising the sequence t-l-p*). In the depicted embodiment, a ninth hairpin monomer C3 comprises a third “assembly complement domain I” (comprising the sequence k-r-h*) and a third “assembly complement domain II” (comprising the sequence n-h-r*).

In the depicted embodiment, the initiator binding domain is typically an input domain, and the assembly domains are typically output domains. In addition, in the depicted embodiment, the assembly and disassembly domains are typically output domains, and the assembly complement domains are typically input domains.

Assembly according to some embodiments of a self-assembly pathway having catalytic geometry is depicted in FIG. 43( b)-(d). An output domain (a*-b*-c*-d*) of the initiator T and the initiator binding domain (a-b-c-d) of the first hairpin monomer A1 are typically substantially complementary. That is, the domain (a*-b*-c*-d*) of the initiator T is able to hybridize to the initiator binding domain (a-b-c-d) of the first hairpin monomer A1.

The initiator T preferably comprises an exposed toehold a*, which is a portion of the domain comprising the sequence a*-b*-c*-d*. Exposed toehold a* of the initiator T is complementary to a sequence segment a of a first hairpin monomer A1. In some embodiments, the initiator binding domain of a first hairpin monomer can comprise an exposed toehold and a portion of the first stem region of the initiator. For example, in FIG. 43 a, the first hairpin monomer A1 has an initiator binding domain a-b-c-d, where a is an exposed toehold, and b-c-d is portion of the first stem region of the first hairpin monomer A1.

Preferably, upon hybridization of the initiator to the exposed toehold of the initiator binding domain of the first hairpin monomer, the second stem region is displaced from the first stem region. This opens the hairpin of the first hairpin monomer. For example, in FIG. 43 b, the initiator T nucleates at the exposed toehold a of the first hairpin monomer A1 by pairing segment a* with a. This induces a strand displacement interaction resulting in the hybridization of the initiator T at a domain a*-b*-c*-d* to the initiator binding domain a-b-c-d of the first hairpin monomer A1.

In the depicted embodiment, upon binding to a complementary monomer, several monomers have a newly exposed single-stranded tail that comprises an assembly domain. For example, monomer A2 has a newly exposed single-stranded tail that comprises the sequence b*-a*-f*-e* and d*-i*-j*. This assembly domain has newly exposed toeholds (e* and d*).

In some embodiments, the first complex can have a newly exposed single-stranded tail that comprises a first “assembly domain I” and a first “assembly domain II” of the first hairpin monomer. For example, as illustrated in FIG. 43 b, the first hairpin monomer A1 develops a newly exposed single-stranded tail that comprises a first “assembly domain I” (comprising the sequence f*-e*-d*-c*) and a “first assembly domain II” (comprising the sequence b*-g*-h*). This first assembly domain has newly exposed toeholds (c* and b*).

In some embodiments, a first assembly domain of a first hairpin monomer can comprise a portion of the loop region and a portion of the second stem region of the first hairpin monomer. For example, in FIG. 43 a, the first “assembly domain I” of first hairpin monomer A1 comprises the sequence f*-e*-d*-c*, where f*-e* is a portion of the loop region and d*-c* is a portion of the second stem region of the first hairpin monomer A1. In the absence of an initiator, the first and second stem regions of the first hairpin monomer are generally hybridized to form a duplex domain of the first hairpin monomer, and the first assembly domain of the first hairpin monomer is generally not available for hybridization to another monomer.

Preferably, upon hybridization of a newly-exposed toehold of the first “assembly domain I” of the first hairpin monomer to the exposed toehold of the first “assembly complement domain” of the second hairpin monomer, the second stem region is displaced from the first stem region. This opens the hairpin of the second hairpin monomer. In the depicted embodiment, the exposed toehold c* of first hairpin monomer A1 nucleates at the exposed toehold c of the second hairpin monomer A2 by pairing segment c* with c (FIG. 43 b). This induces a strand displacement interaction resulting in the hybridization of the first hairpin monomer A1 at the first “assembly domain I” (i.e., f*-e*-d*-c*) to the first “assembly complement domain” (i.e., c-d-e-f) of the second hairpin monomer A2.

In some embodiments, the “second assembly domain I” of a second hairpin monomer can comprise a portion of the loop region and a portion of the second stem region of the second hairpin monomer. For example, in FIG. 43 a, the second “assembly domain I” of second hairpin monomer A2 comprises the sequence b*-a*-f*-e*, where b*-a* is a portion of the loop region and f*-e* is a portion of the second stem region of the second hairpin monomer In the absence of an exposed first “assembly domain I,” the first and second stem regions of the second hairpin monomer are generally hybridized to form a duplex domain of the second hairpin monomer, and the second “assembly domain I” of the second hairpin monomer is generally not available for hybridization to another monomer.

Preferably, upon hybridization of a newly-exposed toehold of the second assembly domain of the second hairpin monomer to the exposed toehold of the second “assembly complement domain” of the third hairpin monomer, the second stem region is displaced from the first stem region. This opens the hairpin of the third hairpin monomer. For example, in FIG. 43 b, the exposed toehold e* of second hairpin monomer A2 nucleates at the exposed toehold e of the third hairpin monomer A3 by pairing segment e* with e (FIG. 43 b). This induces a strand displacement interaction resulting in the hybridization of the second hairpin monomer A2 at the second “assembly domain I” (i.e., e*-f*-a*-b*) to the second assembly complement domain e-f-a-b of the third hairpin monomer A3.

In FIG. 43 b, A3 has a newly exposed single-stranded tail that comprises the “disassembly domain” (comprising the sequence d*-c*-b*-a*) of the third hairpin monomer A3. In some embodiments, the “disassembly domain” of the third hairpin monomer is complementary to a portion of the inhibitor binding domain of the first hairpin monomer.

In some embodiments, the “disassembly domain” of a third hairpin monomer can comprise a portion of the loop region and a portion of the second stem region of the third hairpin monomer. For example, in the depicted embodiment, the disassembly domain of third hairpin monomer A3 comprises the sequence d*-c*-b*-a where d*-c* is a portion of the loop region and b*-a* is a portion of the second stem region of the third hairpin monomer. In the absence of an exposed second “assembly domain I,” the first and second stem regions of the third hairpin monomer are generally hybridized to form a duplex domain of the third hairpin monomer, and the “disassembly domain” of the third hairpin monomer is generally not available for hybridization to another monomer.

As will be appreciated by those of skill in the art, cubes, pyramids, and other shapes can be readily formed using the disclosure herein, to provide for various two or three dimensional shapes to which can be used for imaging and/or detection purposes.

Some embodiments relate to kits for the construction and use of the imaging probes described herein. Some embodiments relate to a kit comprising a collection of hairpin monomers, where one or more hairpin monomers are labeled with one or more fluorophores and/or quenchers. In some embodiments, the kit can include one or more hairpin monomers labeled with fluorescein isothiocyanate (FITC), rhodamine (TRITC), coumarin, Oregon green, eosin, Texas red, cyanine, Nile red, Nile blue, cresyl violet, and oxazine 170. In some embodiments a kit comprises a collection of hairpin monomers, where one or more hairpin monomers comprise an aptamer. In some embodiments, a nucleic acid encoding a fluorescent protein fused to a peptide adaptor can be included. Some embodiments relate to a kit comprising one or more nucleic acids encoding green fluorescent protein (GFP), enhanced green fluorescent protein (EGFP), Emerald, Superfolder GFP, Azami Green, mWasabi, TagGFP, TurboGFP, AcGFP, ZsGreen, T-Sapphire, blue fluorescent protein (BFP), enhanced fluorescent protein (EBFP), EBFP2, Azurite, mTagBFP, cyan fluorescent protein (CFP), enhanced cyan fluorescent protein (ECFP), Cerulean, CyPet, AmCyan1, Midori-Ishi Cyan, TagCFP, mTFP1 (Teal), yellow fluorescent protein (YFP), enhanced yellow fluorescent protein (YFP), Topaz, Venus, mCitrine, YPet, TagYFP, PhiYFP, ZsYellow1, mBanana, orange fluorescent protein (OFP), Kusabira Orange, Kusabira Orange2, mOrange, dTomato, mTangerine, red fluorescent proteins (RFP), DsRed, mRuby, mApple, mStrawberry, AsRed2, JRed, mCherry, HcRed1, mRaspberry, dKeima-Tandem, HcRed-Tandem, mPlum, and AQ143 fused to a peptide adaptor. Some embodiments relate to a kit comprising a collection of hairpin monomers that self assembles into a binary tree. Several embodiments relate to a kit comprising a collection of hairpin monomers that self assembles into a 3-dimensional structure. Some embodiments relate to a kit comprising one or more collections of hairpin monomers that self assemble into a cube, cuboid, dodecahedron, octahedron, pyramid, and tetrahedron or complex polyhedron with 6-10,000 edges. In some embodiments, a kit can include one or more nucleic acids encoding one or more hairpin monomers. Some embodiments relate to a kit comprising a storage media encoding automated design software that can be employed to design hairpin monomers that self-assemble into a prescribed geometric shape. Kits can also include reagents, enzymes, and/or equipment for producing hairpin monomers. Kits can also include packaging. In some embodiments, kits include instructions for practicing a method of the invention.

EXAMPLES

The following examples are offered for illustrative purposes only, and are not intended to limit the scope of the present invention in any way. Indeed, various modifications of the invention in addition to those shown and described herein will become apparent to those skilled in the art from the foregoing description and fall within the scope of the appended claims.

Example 1 System Synthesis

This example illustrates the synthesis and preparation of hairpin monomers.

Nucleic acid synthesis. Nucleic acid, such as, for example, DNA, can be synthesized and purified by various methods known in the art. In some embodiments, purified nucleic acid strands can be reconstituted in, for example, ultrapure water with resistance of at least 18MSΩ. The concentrations of the nucleic acid solutions can then be determined by the measurement of ultraviolet absorption at 260 nm.

Hairpin synthesis. Each hairpin can be synthesized using a variety of methods known in the art. For example, in some embodiments, two nucleic acid pieces can be synthesized and ligated to produce the full hairpin. The ligation can be performed a suitable enzyme, such as, for example, T4 DNA ligase at suitable conditions. For example, the ligation can be performed at room temperature or 16° C. for at least two hours. Ligated strands can be further purified using, for example, denaturing polyacrylamide gel electrophoresis. The bands corresponding to the nucleic acid strands of expected sizes can be visualized by, for example, UV shadowing and excised from the gel. The nucleic acid strands can then be eluted and recovered by ethanol precipitation.

Monomer preparation. For preparation of monomers, concentrated nucleic acid strands can be diluted to suitable reaction conditions. Exemplary reaction conditions can be as follows: 50 mM Na₂HPO₄, 0.5 M NaCl, pH=6.8; or 20 mM Tris, pH=7.6, 2 mM EDTA, 12.5 mM Mg⁺⁺ (1×TAE/Mg⁺⁺ buffer). The hairpins are allowed to anneal under suitable conditions. For example, the hairpins can then annealed by, for example, heating for 5 minutes at 90° C., and then turning off the heating block to allow the system to cool to room temperature (requiring at least 2 hours).

Example 2 System Design Example: Catalytic Formation of 3-Arm Junction

This example illustrates the design procedure for the catalytic 3-arm junction system as presented in FIGS. 2 a and b.

Step (1), Pathway specification. The desired dynamic behavior (FIG. 6 a) is specified using a reaction graph (FIG. 6 b).

Step (2.1), Basic molecular logic implementation. The reaction graph is implemented using the standard motif (FIG. 6 c).

Step (2.2), Padding/clamping. The basic implementation (FIG. 6 c) is modified by adding padding/clamping segments, i.e., segments x, y, z, x*, y* and z* in FIG. 6 d. These segments serve two purposes. First, they serve as ‘padding’ segments to modulate the lengths of the hairpin's exposed toehold, stem, and loop, which permits more flexible dimensioning in the next step. Second, the segments serve as ‘clamps’ to decrease spurious ‘leakage’ reactions in the absence of the initiators. Consider un-clamped hairpin A and hairpin B in FIG. 6 c. When the left-end of hairpin A's stem ‘breathes,’ the 3′ end of the segment b* will be transiently exposed, revealing a partial toe-hold that is complementary to the toe-hold b of hairpin B. This transient toe-hold exposure would permit hairpin A and hairpin B to reach spuriously and form A•B (which would then react with C to form A•B•C). By contrast, the ‘breathing’ of the left end of the clamped hairpin A stem in Figure S3 d exposes x* instead of b* remains sequestered, discouraging spurious reaction between A and B that nucleates at b*.

Step (2.3), Segment dimensioning. The purpose of segment dimensioning is to assign the length of each segment in terms of the number of nucleotides such that under specified conditions, the desired reaction can proceed smoothly while spurious reactions are suppressed. The NUPACK server (www.nupack.org) can be used for dimensioning. For the catalytic 3-arm junction system described here, assigning 6-nt to each segment (FIG. 6 e) stabilizes critical structures in the reaction pathway in the context of a dilute solution of interacting nucleic acid strands.

Step (3), Sequence design. Based on the criteria determined from implementing the reaction graph, primary sequences for the hairpin monomers are designed. The sequences are optimized computationally to maximize affinity and specificity for the formation of the 3-arm junction by minimizing the average number of incorrectly paired bases at equilibrium. The system is synthesized as described in Example 1. Verification of the system is carried out using gel and single-molecule AFM.

Example 3 Execution of the Reaction Graphs for Catalytic 3-Arm/4-Arm Junction Systems

This example illustrates the step-by-step execution of the reaction graphs in FIG. 2 a and e. As shown in FIG. 7 a, Reaction 1 (assembly), a bond is made between the accessible output port of I and the accessible input port of A and both ports are flipped to inaccessible states; the output port of A is flipped to the accessible state (based on the internal logic of node A). Reaction 2 (assembly): a bond is made between the newly accessible output port of A and the accessible input port of B and both ports are flipped to inaccessible states; the output port of B is flipped to the accessible state (based on the internal logic of node B). Reaction 3 (assembly): A bond is made between the newly accessible output port of B and the input port of C and both ports are flipped to inaccessible states; the output port of C is flipped to the accessible state (based on the internal logic of node C). Reaction 4 (disassembly): the bond between the inaccessible output port of I and the inaccessible input port of A is displaced by a bond between the newly accessible blue output port of C and the input port of A; the states of the two output ports are flipped.

The reaction graph in FIG. 7 a contains a k=3 disassembly cycle: input port of A ∘ blue output of A→input port of B ∘ blue output port of B→input port of C ∘ blue output port of C

input port of A. The reaction graph in FIG. 7 b contains a k=4 disassembly cycle: input port of A ∘ blue output of A→input port of B ∘ blue output port of B→input port of C ∘ blue output port of C→input port of D ∘ blue output port of D

input port of A.

Example 4 Catalytic Structure Formation: Catalytic Formation of a 4-Arm Junction

FIGS. 8 a and b depict the reaction graph and reaction schematic for the catalytic formation of a 4-arm junction, respectively. In the absence of initiator I, hairpins A, B, C, and D are kinetically impeded from forming the 4-arm junction that is predicted to dominate at equilibrium. Introduction of I into the system (FIG. 8 b, bottom) activates a cascade of assembly steps with A, B, C, and D followed by a disassembly step in which D displaces I from the complex, freeing I to catalyze the self-assembly of additional branched junctions. The lengths of segments q, q*, r, r*, s, s*, t, and t* are 18 nt; the lengths of the other segments are 6 nt. Hairpins A, B, C, and D are metastable in the absence of the initiator I. The initiator I catalyzes monomers A, B, C, and D to form a 4-arm DNA junction, as follows: (1) segment a* of I nucleates at the toehold a of hairpin A and initiates a strand displacement that results in the opening of hairpin A; (2) newly exposed b* of A nucleates at toehold b of B and results in the opening of B; (3) newly exposed c* of B nucleates at toehold c of C and results in the opening of C; (4a) newly exposed d* of C nucleates at d of hairpin D and results in the opening of D; (4b) D displaces I from A.

Lanes 1-5: A gel shifting assay validates each reaction step depicted in panel (b). Lanes 5-9: Effects of different concentrations of I (1×, 0.5×, 0.25×, 0.1×, and 0×) on the formation of A•B•C•D. 600 nM reactants were incubated at room temperature for 2 hours. Lane 10: A•B•C•D annealed over 2.5 hours (600 nM hairpin species heated at 95° C. for 5 minutes and cooled to room temperature over 2.5 hrs). The 2% agarose gel was prepared in 1×LB buffer (Faster Better Media, LLC) with 0.5 μg/ml ethidium bromide. The gels were run at 150 V for 30 min at room temperature and then visualized using UV transillumination. The hairpins used for these reactions did not contain the 3′ tails (q*, r*, s*, and t*).

Native agarose gel electrophoresis (FIG. 8 c) confirms that the hairpins assemble slowly in the absence of the initiator (Lane 9) and that assembly is dramatically accelerated by the addition of initiator (Lane 5). Disassembly of the initiator enables catalytic turnover as indicated by the nearly complete consumption of hairpins even at sub-stoichiometric initiator concentrations (Lanes 6-8). As in the 3-arm junction case, only minimal assembly is achieved by annealing the hairpin mixture (Lane 10).

AFM imaging of the catalyzed self-assembly product (augmented with strands that extend the duplex portion of each arm as described in the caption) reveals the expected 4-arm junction morphology (FIG. 8 d). To assist in AFM imaging of the 4-arm junction, four strands (Ae, Be, Ce, and De) were incubated with the catalytically formed 4-arm junction A.B.C.D. Note that the duplex portion of the arms of the final structure A•B•C•D•Ae•Be•Ce•De are twice as long as the duplex portion of the arms of A.B.C-D. Two AFM images of A•B•C•D•Ae•Be•Ce•De are presented in FIG. 8 d.

Example 5 AFM Image Analysis

FIGS. 9 a and b depict AFM image analysis of 3-arm/4-arm junctions. Using a B-DNA model where one helical turn contains 10.5 base pairs and measures 3.4 nm, the expected arm length for the 3-arm junction was calculated as follows: (24/10.5)×3.4 nm=7.8 nm. Similarly, the arm length for the 4-arm junction is calculated to be 7.8+7.8=15.6 nm. The measured lengths of the arms are roughly consistent with the calculated lengths. FIGS. 10 a and b show AFM images with a larger field of view for 3-arm (a) and 4-arm (b) junctions.

Example 6 Design for the Catalytic Formation of a k-Arm Junction

The catalytic system described in FIG. 2 and FIG. 8 can, in principle, be generalized to a system capable of the catalytic formation of a k-arm junction. FIGS. 11 a and b describe the reaction graph and the secondary structure schematic for the catalytic formation of a k-arm junction. Hairpins H₁, H₂, . . . , H_(k) are metastable in the absence of the initiator I. The initiator I catalyzes monomers H₁, H₂, . . . , H_(k) to form a k-arm DNA junction.

FIGS. 12 a-c depict an example when k=6. In FIGS. 12 b and c, hairpins H₁, H₂, H₃, H₄, H₅ and H₆ are metastable in the absence of the initiator I. The initiator I catalyzes monomers H₁, H₂, H₃, H₄, H₅ and H₆ to form a 6-arm DNA junction as follows. Step 1: segment a*₁ of I nucleates at the toehold a₁ of hairpin H₁ and initiates a strand displacement that results in the opening of hairpin H₁. Step 2: the newly exposed a*₂ of H₁ nucleates at the toehold a₂ of hairpin H₂ and opens hairpin H₂. Step 3: the newly exposed a*₃ of H₂ nucleates at the toehold a₃ of hairpin H₃ and opens hairpin H₃. Step 4: the newly exposed a*₄ of H₃ nucleates at the toehold a₄ of hairpin H₄ and opens hairpin H₄. Step 5: the newly exposed a*₅ of H₄ nucleates at the toehold a₅ of hairpin H₅, and opens hairpin H₅. Step 6: the newly exposed a*₆ of H₅, nucleates at the toehold a₆ of hairpin H₆ and opens hairpin H₆. Step 7: H₆ displaces I from H₁.

Example 7 Catalytic Circuitry

FIG. 13 describes the step-by-step execution of the reaction in FIG. 3 a. The reaction starts at solid arrow (1) that connects the accessible output port of I and the accessible input port of A. Note that by convention, the two arrows entering the same input port of A depict parallel processes on separate copies of the nodal species.

Reaction 1 (assembly): A bond is made between the accessible output port of I and the accessible input port of A and both ports are flipped to inaccessible states; the output port of A is flipped to the accessible state (based on the internal logic of node A).

Reaction 2 a (assembly): A bond is made between the newly accessible output port of A and the accessible input port of Band both ports are flipped to inaccessible states; the two output ports of B are flipped to accessible states (based on the internal logic of node B).

Reaction 2 b (disassembly): The bond between the inaccessible output port of I and the inaccessible input port of A is displaced by a bond between the newly accessible blue output port of B and the input port of A; the states of the two output ports are flipped.

Reaction 3 (assembly): A bond is made between the newly accessible green output port of B and the accessible input port of C and both ports are flipped to inaccessible states; the output port of C is flipped to the accessible state (based on the internal logic of node C).

Reaction 4 a (assembly): A bond is made between the newly accessible output port of C and the accessible input port of D and both ports are flipped to inaccessible states; the output ports of D are flipped to accessible states (based on the internal logic of node D).

Reaction 4 b (disassembly): The bond between the inaccessible green output port of B and the inaccessible input port of C is displaced by a bond between the newly accessible blue output port of D and the input port of C; the states of the two output ports are flipped.

Reaction 5 (assembly): A bond is made between the newly accessible green output port of D and the accessible input port of A and both ports are flipped to inaccessible states; the output port of A is flipped to the accessible state (based on the internal logic of node A).

Reaction 6 a (assembly): A bond is made between the newly accessible output port of A and the accessible input port of B and both ports are flipped to inaccessible states; the output ports of B are flipped to accessible states (based on the internal logic of node B).

Reaction 6 b (disassembly): The bond between the inaccessible green output port of D and the inaccessible input port of A is displaced by a bond between the newly accessible blue output port of B and the input port of A; the states of the two output ports are flipped.

FIG. 14 describes the detailed reaction flow of the autocatalytic system described in FIG. 3. FIG. 15 a-c describe additional intermediate steps. Steps 1-2 are the initiation stage; steps 3-6 are the exponential amplification stage.

Step 1: the toehold a* of I nucleates at the toehold a of A, resulting in the opening of the hairpin and the formation of the product I•A.

Step 2: I•A, with b* newly exposed, opens hairpin B (step 2a); B subsequently displaces I from A (step 2b), producing A•B and bringing the system to the exponential amplification stage. The single-stranded tail (v*-d*-y*-u*-c*) of A•B next catalyzes C and D to form C•D (in steps 3 and 4).

Step 3: A•B, with c* newly exposed, opens hairpin C.

Step 4: A•B•C, with d* newly exposed, opens hairpin D (step 4a); D subsequently displaces C from B, separating A•B and C•D (step 4b). The single-stranded tail (a*-x*-v*-b*-y*) of C•D is identical to I and next catalyzes A and B to form A•B (in steps 5 and 6).

Step 5: C•D, with a* newly exposed, opens hairpin A.

Step 6: C•D•A, with b* newly exposed, opens B (step 6a); B subsequently displaces A from D, separating C•D and A•B (step 6b).

FIGS. 16 a and b depict a stepping gel for the autocataytic system. The hairpins used for these reactions were synthesized and purified by IDT DNA and used without further purification. The annealed samples were annealed at 2 μM reactant concentrations: heating at 95° C. for 5 minutes followed by cooling to room temperature over approximately 2.5 hours. The room temperature reactions were conducted with each reactant species at 1 μM concentration. Consider the sample, (AI)+B, in Lane 5. The sample was prepared by first annealing a mix containing 2 μM A and 2 μM I to produce (AI). Then 2 μL of (AI), at 2 μM concentration, was mixed with 2 μL of B at 2 μM concentration and allowed to react at room temperature for 15 minutes. Lanes 1 and 14 are 20-1000 by DNA ladders (Bio-Rad). The 5% native polyacrylamide gel was prepared in 1×TAE/Mg⁺⁺ buffer (20 mM Tris, pH=7.6, 2 mM EDTA, 12.5 mM Mg⁺⁺). The samples were loaded with 10% glycerol. The gel was run at 100 V for 90 minutes at room temperature, post-stained with 0.5 μg/mL ethidium bromide, and visualized by UV transillumination. The blue line delineates the boundary between two gels.

The autocatalytic system was validated on a step-by-step basis using native polyacrylamide gel electrophoresis (PAGE) (FIG. 16 b):

Step 1. Hairpin A reacts with initiator I and produces a band that corresponds to product A•I (Lane 3), which migrates at about the same speed as the annealed product A•I (Lane 4), as expected.

Step 2. Annealed sample A•I reacts with hairpin B and produces a band that corresponds to product A•B (Lane 5), which migrates at about the same speed as the annealed product A•B (Lane 6), as expected.

Step 3. Annealed sample A•B reacts with hairpin C and produces a band that corresponds to product A•B•C (Lane 7), which migrates at about the same speed as the annealed product A•B•C (Lane 8), as expected.

Step 4. Annealed sample A•B•C reacts with hairpin D and produces a band that corresponds to product A•B and C•D (Lane 9), which migrates at about the same speed as the annealed product A•B (Lane 6) and the annealed product C•D (Lane 10), as expected.

Step 5. Annealed sample C•D reacts with hairpin A and produces a band that corresponds to product C•D•A (Lane 11), which migrates at about the same speed as the annealed product C•D•A (Lane 12), as expected.

Step 6. Annealed sample C•D•A reacts with hairpin B and produces a band that corresponds to product C•D and A•B (Lane 13), which migrates at about the same speed as the annealed product C•D (Lane 10) and the annealed product A•B (Lane 6), as expected.

System kinetic analysis and data analysis is described in Yin et al., Nature 451(7176), 318-322; Supplementary Information pages 1-49 (2008), which is incorporated herein by reference in its entirety.

Example 8 Nucleated Dendritic Growth

FIG. 17 depicts the execution of the reaction graph of FIG. 4 a. The multiple arrows entering the same input port depict parallel processes on separate copies of the nodal species. The parallel processes are not synchronized and hence it is possible, for example, that after A1 assembles with A2, the assembly of A2 with A3 occurs before the assembly of A1 with B2.

FIG. 18 and FIG. 19 present the detailed reaction schematic of the nucleated dendritic growth system described in FIG. 4. In the absence of the initiator I, hairpin monomers co-exist metastably. The initiator I triggers the system to self-assemble into a binary tree of a prescribed size.

Step 1: the toehold a* of the initiator I nucleates at the toehold a of hairpin A1, resulting in the opening of A1 and the formation of the first generation dendrimer, G1.

Step 2: A1, with b* and c* newly exposed, opens hairpins A2 and B2, producing the second generation dendrimer, G2. Note that now A2 and B2 reveal single-stranded tails of identical sequences.

Step 3: A2 and B2, with d* and e* newly exposed, open hairpins A3 and B3, producing G3.

Step 4: each copy of A3 and B3, with its newly exposed f* and g*, opens hairpins A4 and B4, producing G4.

Step 5: each copy of A4 and B4, with its newly exposed h* and i*, opens hairpins AS and B5, producing G5.

Example 9 Quantitative Amplification Gel and AFM Image Analysis

FIG. 20 demonstrates that the concentration of dendrimer depends linearly on the concentration of the initiator in the system. The top panel of FIG. 20 shows different concentrations of initiator incubated with all hairpin species (A1, A2, B2, 91 nM; the concentration doubles for each subsequent generation of hairpins). The gel shown in FIG. 20 is used to measure fluorescence emission from Cy5, which is used to label hairpin A1. In the figure, D denotes dendrimers; M denotes monomers. The bottom panel of FIG. 20 shows linear fit between the fluorescence signal of the dominant reaction product versus the concentration of initiator. Data from three independent experiments are denoted respectively by blue crosses, red diamonds, and green circles. Each set of data is normalized by the signal obtained at 70 nM initiator concentration.

Using a B-DNA model where one helical turn contains 10.5 base pairs and measures 3.4 nm, we calculate the expected arm length for the duplex formed by Al and I to be 25/10.5×3.4 nm=8.1 nm and the approximate length of all the other duplex segments to be 50/10.5×3.4 nm=16.2 nm. FIG. 21 shows the image analysis for G3 and G4 dendrimers. The small images are screenshots of the measurement section files. The distance between the two red arrowheads is listed above the image. The blue arrows point to the 4-arm junction in both the schematic and the images and help to relate the images to the schematic. FIG. 22 shows the image analysis for G5 dendrimers. The measured lengths of the arms are roughly consistent with the calculated lengths. In FIG. 22, the distance between the two red arrowheads is listed above the image. The blue arrows point to the 5-arm/4-arm junctions in both the schematic and the images and help to relate the images to the schematic. Note that the duplex A•I is not visible for the image in the left panel, likely due to damage during sample preparation or AFM scanning. FIG. 23 shows a large field-of-view AFM image of the G5 system. As seen by FIGS. 21-23, in most AFM images, only the duplex portions of the dendrimer are visible.

Example 10 Autonomous Locomotion

FIG. 24 a-b depicts the step-by-step execution of the reaction graph for the walker. In FIG. 24 a-b, the reaction steps corresponding to the processive sub-population of walkers are shown in purple. In the initial conditions prior to Step 1, the input ports of the A nodes at sites 1 and 2 are bound to the output ports of the I nodes on the bipedal walker. Execution begins with an assembly reaction between the accessible output port on either of these A nodes and the accessible input port on B. In the top route of Step 1, B assembles with A at site 1, resulting in the disassembly of the trailing I from A, which is then free to assemble with A at site 3, moving the walker one step down the track and bringing the system to Step 2. Alternatively, a B node could bind to A at site 2 prior to the assembly of I with A at site 3, resulting in the disassembly of the walker from the track. The walker could then diffuse through the bulk solution and re-attach to the same track or another track at any A monomer that has not yet been occupied. In the bottom route of Step 1, node B assembles with node A at site 2, resulting in the disassembly of the leading I from A. Due to geometric constraints (inextensible walker torso and rigid track backbone), the walker cannot attach to site 1 and site 3 simultaneously and hence will eventually detach from the track when a B node assembles with A at site 1. Similarly, in Step 2 and Step 3, processive stepping occurs stochastically for a sub-population of walkers. In Step 4, the walker will disassemble from track.

According to FIG. 24 a-b, the initial bond between the output port of I and the input port of A indicates that an assembly reaction has already occurred prior to the execution of the reaction graph. As noted above, static structural elements can impose geometrical constraints on the execution of the reaction graph. In the reaction graph depicted here, the gray structural elements represent a rigid track backbone and an inextensible walker torso; their relative dimensions imply that when one I node is attached to an A node on the track, the other I node can only interact with the A node to either side.

A secondary structure schematic of the walker system of FIG. 5 is shown in FIG. 25. FIG. 26 a-b depict the step-by-step secondary structure schematic corresponding to the reaction graph of FIG. 24 a-b. A more detailed view of Step 1 is shown in FIG. 27 a-d.

The walker system was assembled in four steps (FIG. 28 a).

Step 0. The walker (W) was assembled by annealing strands W1-BHQ1 and W2-BHQ1 as follows: heat the mixture at 95° C. for 5 minutes and slowly cool to room temperature over the course of 4 hours.

Step 1. Hairpins S1 and S4 were mixed with track strands S2, S3, and S5, then annealed to produce Track 1 (T1) as follows: heat the system at 95° C. for 5 minutes; slowly cool to room temperature over the course of 4 hours.

Step 2. T1 and the pre-assembled walker (W) were incubated at room temperature for 2 hours to produce T1+W.

Step 3. Hairpins S6, S9, and S11 were mixed with track strands S7, S8, S10, and S12, then annealed to produce Track 2 (T2) as follows: heat the system to 95° C. for 5 minutes; slowly cool to room temperature over the course of 4 hours. For the bipedal and monopedal landing control experiments, the S7 track strand is replaced by S7 truncated so that T1 and T2 remain disjoint.

Step 4. T2 and T1+W were incubated at room temperature for 3 hours to produce the final system, T1+W+T2.

Native agarose gel electrophoresis demonstrates a band shifting pattern that confirms on a step-by-step basis the correct assembly of the walker system. (FIG. 28 b). Samples were annealed and assembled in reaction buffer (4 mM MgCl₂, 15 mM KCl, and 10 mM Tris-HCl, pH=8.0) with all species at 0.5 μM. A 3% native agarose gel was prepared in 1×LB buffer (Faster Better Media, LLC). Samples were loaded with 2×SYBR Gold stain (Invitrogen) and 10% glycerol. The gel was run at 200 V for 40 minutes at room temperature and visualized using an FLA-5100 imaging system (Fuji Photo Film Co., Ltd.)

Example 11 Characterization of the Fuel System

This example describes the fuel system that powers the walker system, which is depicted in FIGS. 29 a and b. Here, hairpins A and B co-exist metastably in the absence of catalyst 1. Catalyst I catalyzes A and B to form duplex AB (FIG. 29 a). Native gel electrophoresis (FIG. 29 b) confirms that the hairpins assemble slowly in the absence of the initiator (Lane 7) and that the assembly is dramatically accelerated by the addition of initiator (Lane 3). Disassembly of the initiator enables catalytic turnover as indicated by the nearly complete consumption of hairpins even at sub-stoichiometric initiator concentrations (Lanes 4-6).

Agarose gel electrophoresis demonstrates catalytic formation of the DNA duplex (FIG. 29 b). The hairpins were prepared in reaction buffer (4 mM MgCb, 15 mM KCl, and 10 mM Tris-HCl, pH=8.0) using a snap-cooling procedure: heating at 90° C. for 5 minutes and cooling on ice for 1 minute. The hairpins were allowed to equilibrate at room temperature for 30 minutes before use. Lanes 1-3: A gel shifting assay validates each reaction step depicted in panel (a). Lanes 3-7: Effects of different concentrations of I (1×, 0.5×, 0.25×, 0.1×, and 0×) on the formation of A.B. Reactants were incubated at 1 μM at room temperature for 2 hours. Lane 8: A.B annealed over 2.5 hours (1 μM hairpin species heated at 95° C. for 5 minutes and cooled to room temperature over 2.5 hrs). Upon completion of the reaction, the samples were loaded with 5×SYBR Gold stain (Invitrogen) and 10% glycerol into a 2% native agarose gel, prepared with 1×LB buffer (Faster Better Media, LLC). The gel was run at 350 V for 10 minutes at room temperature and visualized using an FLA-5100 imaging system (Fuji Photo Film Co., Ltd.).

Fluorescence quenching experiments was carried out to investigate catalyst recovery, and is described, in Yin et al., Nature 451(7176), 318-322; Supplementary Information pages 1-49 (2008) at page 31-37, which is incorporated herein by reference in its entirety.

Example 13 Synthesis of DNA, Hairpins and Monomers

This example illustrates the synthesis of DNA, hairpins and monomers used in the Examples.

DNA was synthesized and purified by Integrated DNA Technologies. The purified DNA strands were reconstituted in ultrapure water (resistance of 18 MΩ-cm). The concentrations of the DNA solutions were determined by the measurement of ultraviolet light absorption at 260 nm.

Each hairpin was synthesized as two pieces which were then ligated to produce the full hairpin. The ligation was performed using T4 DNA ligase (New England Biolabs) at either room temperature or 16° C. for a minimum of two hours. Ligated strands were further purified using denaturing polyacrylamide gel electrophoresis. The bands corresponding to the DNA strands of expected sizes were visualized by UV shadowing and excised from the gel. The DNA strands were then eluted and recovered by ethanol precipitation. (3) Monomer preparation. The concentrated DNA strands were diluted to reaction conditions: 50 mM Na₂HPO₄, 0.5 M NaCl, pH=6.8 for species in FIG. 2 and Figure S4; and 20 mM Tris, pH=7.6, 2 mM EDTA, 12.5 mM Mg⁺⁺ (1×TAE/Mg⁺⁺ buffer) for species in FIG. 3, Figure S12, and FIG. 4. The hairpins were then annealed by heating for 5 minutes at 90° C., and then the heating block was turned off to allow the system to cool to room temperature (requiring at least 2 hours).

Commercially available synthetic single-stranded DNA oligos can be impure and contain incorrectly synthesized strands. The presence of such erroneous strands can contribute to leakage during self-assembly. In some embodiments, to improve strand purity and hence decrease system leakage, the following enzyme-based ligation method can be used to synthesize the hairpin monomers: two constituent segments of a hairpin are synthesized and purified separately and ligated to produce the full hairpin (FIG. 30). Significant reduction of system leakage in the ligation-based system is observed, as compared to the un-ligated system.

The observed error reduction can be attributed to the following two mechanisms. First, longer DNA strands contain more errors than shorter fragments, since the shorter fragments can be purified to a higher purity. Behlke et al., Tech. Rep., Integrated DNA Technologies (2005). As such, the two constituent segments contain fewer total errors than the full strand. Second, for T4 ligase mediated ligation of Ha and Hb, the successful ligation depends on the correct juxtaposition of the 5′ end of fragment Hb with the 3′ end of fragment Ha. This requirement provides an additional error reduction mechanism: DNA segments with errors in the regions adjacent to the nick position are not ligated successfully and are eliminated during the subsequent gel purification.

Example 14 Gel Electrophoresis

This example illustrates electrophoresis analysis of the self-assembly systems.

For the gel in FIG. 2 c, 12 μL of each 3 μM hairpin species were mixed by pipetting. 6 μL of this master mix was aliquoted into 5 separate tubes. To these tubes were added 2 μL of either 3 μM I (Lane 1), 1.5 μM I (Lane 2), 0.75 μM I (Lane 3), 0.3 μM I (Lane 4), or 1× reaction buffer (50 mM Na₂HPO₄, 0.5 M NaCl, pH=6.8) (Lane 5) to reach a total reaction volume of 8 μL. The samples were then mixed by pipetting and allowed to react for 2.5 hours at room temperature. The annealed reaction (Lane 6), prepared 0.5 hour in advance, was made by mixing 2 μL of each hairpin with 2 μL of the 1× reaction buffer, and then annealing as described in monomer preparation. A 2% native agarose gel was prepared for use in 1×LB buffer (Faster Better Media, LLC). 1 μL of each sample was then mixed with 1 μL of 5×SYBR Gold loading buffer: 50% glycerol/50% H₂O/SYBR Gold (Invitrogen) and loaded into the gel. The gel was run at 350 V for 10 minutes at room temperature and imaged using an FLA-5100 imaging system (Fuji Photo Film Co., Ltd.).

For the gel in FIG. 4 c, hairpins were annealed at the following concentrations: A1, A2, B2, A3, and B3 at 1 μM; A4 and B4 at 2 μM; A5 and B5 at 4 μM. The initiator I was prepared at 800 nM. The following sample mixtures were prepared: Lane 1, A1; Lane 2, I+A1; Lane 3, I+A1+A2+B2; Lane 4, I+A1+A2+B2+A3+B3; Lane 5, I+A1+A2+B2+A3+B3+A4+B4; Lane 6, I+A1+A2+B2+A3+B3+A4+B4+A5+B5; Lane 7, A1+A2+B2+A3+B3+A4+B4+A5+B5. Here, I, A1, A2, and B2 were added at 1 μL; A3, B3, A4, B4, A5, and B5 at 2 μL. 1× reaction buffer (20 mM Tris, pH=7.6, 2 mM EDTA, 12.5 mM Mg⁺⁺) was added to bring the total volume of each sample to 16 μL. The samples were mixed by pipetting and allowed to react for 2 hours at room temperature. A 1% native agarose gel was prepared in 1×LB buffer. 8 μL of each sample were added to 2 μL 5×SYBR Gold loading buffer. 8 μL of the sample/loading-buffer mix were then loaded into the gel. The gel was run at 350 V for 10 minutes at room temperature and then imaged using an FLA-5100 imaging system. For the reactions in FIG. 4 d, the hairpins were mixed to reach the following final concentration: A1-Cy5, A2, B2, 100 nM; A3, B3, 200 nM; A4, B4, 400 nM; A5, B5, 800 nM. 9 μL of this mix were then aliquoted into 10 separate tubes. To these tubes was added either 1×TAE/Mg⁺⁺ reaction buffer or the initiator I to give the indicated final concentration of I and a final volume of 11 μL. The samples were mixed by pipetting and then allowed to react for 1 hour at room temperature. The sample was then mixed with 5×LB loading buffer (Faster Better Media, LLC) to reach 1× loading buffer concentration (8 μL sample, 2 μL loading buffer). The sample/loading buffer mix was loaded into a 1% native agarose gel prepared in 1×LB buffer. The gel was run at 350 V for 10 minutes at room temperature and then imaged and quantified using an FLA-5100 imaging system. The experiments were performed with 10 μM inert 25-nt poly-T carrier strands in the reaction solution.

Example 15 AFM Imaging

This example illustrates AFM imaging of the self-assembly systems.

AFM images were obtained using a multimode scanning probe microscope (Veeco Instruments Inc.), equipped with a Q-Control module for analog AFM systems (Atomic Force F&E GmbH). The images were obtained in liquid phase under tapping mode using DNP-S oxide sharpened silicon nitride cantilevers (Veeco Instruments Inc.). Samples were first diluted in 1×TAE/Mg⁺⁺ buffer to achieve the desired imaging density. A 20 μL drop of 1×TAE/Mg⁺⁺ and a 5 μL drop of sample were applied to the surface of freshly cleaved mica and allowed to bind for approximately 2 minutes. Supplemental 15-30 mM Ni⁺⁺ was added to increase the strength of DNA-mica binding. Before placing the fluid cell on top of the mica puck, an additional 15-20 μL of 1×TAE/Mg⁺⁺ buffer was added to the cavity between the fluid cell and the AFM cantilever chip to avoid bubbles.

Example 16 Fluorescence Experiments

This example illustrates fluorescence experiments with the self-assembly systems.

Catalytic circuitry. Fluorescence data were obtained using a QM-6/2005 steady state spectrofluorometer (Photon Technology International), equipped with a Turret 400™ four-position cuvette holder (Quantum Northwest) and 3.5 mL QS quartz cuvettes (Hellma GmbH & Co. KG). The temperature was set to 25° C. The excitation and emission wavelengths were set to 520 nm (2 nm bandwith) and 540 nm (4 nm bandwidth), respectively. For the experiments in FIG. 3 c, hairpin monomers, A, B, C, and D, and initiator, I, were prepared separately as described above. 40 μL 1 μM A were added to 1800 μL 1×TAE/Mg⁺⁺ buffer and mixed by rapid pipetting 8 times using a 1 mL tip. The baseline signal was recorded for ˜16 minutes. Then 40 μL of 1 μM B, C, and D, and the appropriate concentration of I (or 1×TAE/Mg⁺⁺ buffer in the case of 0×I) were added to the cuvette (to reach the target concentrations described in FIG. 3 c) and mixed by rapid pipetting 8 times using a 1 mL tip. The control with 20 nM A alone was monitored continuously. The final volume was 2 mL for all experiments. The experiments were performed with 10 μM inert 25-nt poly-T carrier strand in the individual hairpin and initiator stock solutions and ˜1 μM inert 25-nt poly-T carrier strands in the final reaction solution.

Autonomous locomotion. Fluorescence experiments were performed at 21° C. using the same spectrofluorometer as above. Two 3.5 mL QS quartz cuvettes (Hellma GmbH & Co. KG) were used in each set of experiments. Excitation and emission wavelengths were set to 492 nm and 517 nm (for FAM), 527 nm and 551 nm (for JOE), and 558 nm and 578 nm (for TAMRA), respectively, with 4 nm bandwidths. The assembly of the walker system is described above. Hairpin B was snap cooled in the reaction buffer (4 mM MgCl₂, 15 mM KCl, and 10 mM Tris-HCl, pH=8.0): heating at 95° C. for 90 seconds, rapid cooling at room temperature, allowed to sit at room temperature for 30 minutes before use. The system was assembled using 4 nM track and 3.5 nM bipedal walker. A sub-stochiometric amount of walker was used to ensure that no free-floating walker would bind to hairpin A on the track. For the same reason, sub-stoichiometric monopedal walker (7 nM) was used in the diffusion experiments. The final concentration of hairpin B was 20 nM, which was equimolar with the five A hairpins on the track (5×4 nM=20 nM). The assembled track was first introduced to record the fluorescence baselines for FAM, JOE, and TAMRA. Hairpin B was then introduced and mixed 100 times by rapid pipetting to start walker locomotion.

Example 17 DNA Sequences

The DNA sequences for the systems described in the Examples are presented both as secondary structure schematics in FIGS. 31-35 and as text sequences annotated with segment names.

For each hairpin sequence X, the two segments that are ligated to produce X are indicated as Xa and Xb. Strand modifications are indicated as follows:

-   -   5′ phosphorylation: /5Phos/;     -   3′6-carboxyfluorescein: /36FAM/;     -   5′6-carboxyfluorescein: /56FAM/;     -   5′6-carboxy-4′, 5′ dichloro-2′,7′-dimethoxyfluorescein (NETS         Ester): /5JOEN/;     -   5′ tetrachlorofluorescein: /5 STET/;     -   5′ carboxytetramethylrhodamine (NHS Ester): /5TMRN/;     -   3′ black hole quencher-1: /3BHQ_(—)1/

Catalytic 3-arm junction system. The sequences are listed below as text sequences annotated with segment names.

A: a-x-b-y-z*-c*-y*-b*-x* GCTTGA-GATGTT-AGGGAG-TAGTGC-TCCAAT-CACAAC-GCACTA-CTCCCT-AACATC (SEQ ID NO: 1) Aa: GCTTGAGATGTTAGG (SEQ ID NO: 2) Ab: /5Phos/GAGTAGTGCTCCAATCACAACGCACTACTCCCTAACATC (SEQ ID NO: 3) B: b-y-c-z-x*-a*-z*-c*-y* AGGGAG-TAGTGC-GTTGTG-ATTGGA-AACATC-TCAAGC-TCCAAT-CACAAC-GCACTA (SEQ ID NO: 4) Ba: AGGGAGTAGTGCGTT (SEQ ID NO: 5) Bb: /5Phos/GTGATTGGAAACATCTCAAGCTCCAATCACAACGCACTA (SEQ ID NO: 6) C: c-z-a-x-y*-b*-x*-a*-z* GTTGTG-ATTGGA-GCTTGA-GATGTT-GCACTA-CTCCCT-AACATC-TCAAGC-TCCAAT (SEQ ID NO: 7) Ca: GTTGTGATTGGAGCT (SEQ ID NO: 8) Cb:/5Phos/TGAGATGTTGCACTACTCCCTAACATCTCAAGCTCCAAT (SEQ ID NO: 9) I: y*-b*-x*-a* GCACTA-CTCCCT-AACATC-TCAAGC (SEQ ID NO: 10)

Catalytic 4-arm junction system. The sequences are listed below as text sequences annotated with segment names.

A: a-w-b-x-y*-c*-x*-b*-w*-q* GCTTGA-GATGTT-AGGGAG-TAGTGC-TCCAAT-CACAAC-GCACTA-CTCCCT-AACATC- (SEQ ID NO: 11) AACCACCACCAACCACCC Aa: GCTTGAGATGTTAGGGAGTAGTGCTCCAATCACAACGCACTACTCC (SEQ ID NO: 12) Ab: /5Phos/CTAACATCAACCACCACCAACCACCC (SEQ ID NO: 13) B: b-x-c-y-x*-d*-y*-c*-x*-r* AGGGAG-TAGTGC-GTTGTG-ATTGGA-ACTCAT-CTACCG-TCCAAT-CACAAC-GCACTA- (SEQ ID NO: 14) ACAACACACACAAACCAC Ba: AGGGAGTAGTGCGTTGTGATTGGAACTCATCTACCGTCCAATCAC (SEQ ID NO: 15) Bb: /5Phos/AACGCACTAACAACACACACAAACCAC (SEQ ID NO: 16) C: c-y-d-z-w*-a*-z*-d*-y*-s* GTTGTG-ATTGGA-CGGTAG-ATGAGT-AACATC-TCAAGC-ACTCAT-CTACCG-TCCAAT- (SEQ ID NO: 17) ATCCTTCCCTTCCTCTCC Ca: GTTGTGATTGGACGGTAGATGAGTAACATCTCAAGCACTCATCTAC (SEQ ID NO: 18) Cb: /5Phos/CGTCCAATATCCTTCCCTTCCTCTCC (SEQ ID NO: 19) D: d-z-a-w-x*-b*-w*-a*-z*-t* CGGTAG-ATGAGT-GCTTGA-GATGTT-GCACTA-CTCCCT-AACATC-TCAAGC-ACTCAT- (SEQ ID NO: 20) TCTCTTCTTCTCTTCTTC Da: CGGTAGATGAGTGCTTGAGATGTTGCACTACTCCCTAACATCTCAA (SEQ ID NO: 21) Db: /5Phos/GCACTCATTCTCTTCTTCTCTTCTTC (SEQ ID NO: 22) I: x*-b*-w*-a* GCACTA-CTCCCT-AACATC-TCAAGC (SEQ ID NO: 23) Ae: q-w GGGTGGTTGGTGGTGGTT-GATGTT (SEQ ID NO: 24) Be: r-x GTGGTTTGTGTGTGTTGT-TAGTGC (SEQ ID NO: 25) Ce: s-y GGAGAGGAAGGGAAGGAT-ATTGGA (SEQ ID NO: 26) De: t-z GAAGAAGAGAAGAAGAGA-ATGAGT (SEQ ID NO: 27)

Autocatalytic system. The sequences are listed below as text sequences annotated with segment names.

A: x*-v*-b*-y*-u*-c*-a*-x*-y-b-v-x-a ACAACT-GAACAC-GTTAGA-CCACTT-CCATCC-TCGCAA-ATCTCC-ACAACT-AAGTGG-TCTAAC- (SEQ ID NO: 28) GTGTTC-AGTTGT-GGAGAT Aa-TET: /5TET/TT-ACAACTGAACACGTTAGACCACTTCCATCCTCGCAAATCTCCACAACTAAGTGGTCTAAC (SEQ ID NO: 29) Ab-BHQ1: /5Phos/GTGTTCAGTTGTGGAGAT/3BHQ_1/ (SEQ ID NO: 30) B: v*-d*-y*-u*-c*-a*-x*-v*-b*-y*x-a-c-u-y-b GAACAC-TGCTCT-CCACTT-CCATCC-TCGCAA-ATCTCC-ACAACT-GAACAC-GTTAGA-CCACTT- (SEQ ID NO: 31) AGTTGT-GGAGAT-TTGCGA-GGATGG-AAGTGG-TCTAAC Ba: GAACACTGCTCTCCACTTCCATCCTCGCAAATCTCCACAACTGAACACGTTAGACCACTTAGTTGTGGAGATTTG (SEQ ID NO: 32) CGA Bb: /5Phos/GGATGGAAGTGGTCTAAC (SEQ ID NO: 33) C: c-u-y-d-v-u*-c*-a*-x*-v*-d*-y*-u* TTGCGA-GGATGG-AAGTGG-AGAGCA-GTGTTC-CCATCC-TCGCAA-ATCTCC-ACAACT-GAACAC- (SEQ ID NO: 34) TGCTCT-CCACTT-CCATCC Ca: TTGCGAGGATGGAAGTGGAGAGCAGTGTTCCCATCCTCGCAAATCTCCACAACTGAACACTGCTCTCC (SEQ ID NO: 35) Cb: /5Phos/ACTTCCATCC (SEQ ID NO: 36) D: d-v-x-a-c-u-v*-d*-y*-u*-c*-a*-x*-v*-b*-y* AGAGCA-GTGTTC-AGTTGT-GGAGAT-TTGCGA-GGATGG-GAACAC-TGCTCT-CCACTT-CCATCC- (SEQ ID NO: 37) TCGCAA-ATCTCC-ACAACT-GAACAC-GTTAGA-CCACTT Da: AGAGCAGTGTTCAGTTGTGGAGATTTGCGAGGATGGGAACACTGCTCTCCACTTCCATCCTCGCAAATCTCC (SEQ ID NO: 38) Db: /5Phos/ACAACTGAACACGTTAGACCACTT (SEQ ID NO: 39) I: a*-x*-v*-b*-y* ATCTCC-ACAACT-GAACAC-GTTAGA-CCACTT (SEQ ID NO: 40)

Nucleated dendritic growth system. The sequences are listed below as text sequences annotated with segment names. A1 b-Cy5 (together with A1 a) is used to synthesize Cy5 labeled hairpin A1.

A1: a-x-c-b-x-y-x*-d*-e*-x*-b*-c*-x*-d*-e*-x* CAAACTC-TT-ATCTATC-TCTGCCA-TT-TT-AA-TGCAATG-TCACGGT-AA-TGGCAGA-GATAGAT-AA- (SEQ ID NO: 41) TGCAATG-TCACGGT-AA A1a: CAAACTCTTATCTATCTCTGCCATTTTAATGCAATGTCACGGTAATGGCAGA (SEQ ID NO: 42) A1b: /5Phos/GATAGATAATGCAATGTCACGGTAA (SEQ ID NO: 43) A1b-Cy5: /5Phos/GATAGATAATGCAATGTCACGGTAA-TT/3Cy5sp/ (SEQ ID NO: 44) A2: b-x-e-d-x-y-x*-f*-g*-x*-d*-e*-x*-f*-g*-x* TCTGCCA-TT-ACCGTGA-CATTGCA-TT-TT-AA-GCTACAG-GACTACG-AA-TGCAATG-TCACGGT-AA- (SEQ ID NO: 45) GCTACAG-GACTACG-AA A2a: TCTGCCATTACCGTGACATTGCATTTTAAGCTACAGGACTACGAATGCAATG (SEQ ID NO: 46) A2b: /5Phos/TCACGGTAAGCTACAGGACTACGAA (SEQ ID NO: 47) A3: d-x-g-f-x-y-x*-h*-i*-x*-f*-g*-x*-h*-i*-x* CATTGCA-TT-CGTAGTC-CTGTAGC-TT-TT-AA-GTATCAG-ATCGCCG-AA-GCTACAG-GACTACG-AA- (SEQ ID NO: 48) GTATCAG-ATCGCCG-AA A3a: CATTGCATTCGTAGTCCTGTAGCTTTTAAGTATCAGATCGCCGAAGCTACAG (SEQ ID NO: 49) A3b: /5Phos/GACTACGAAGTATCAGATCGCCGAA (SEQ ID NO: 50) A4: f-x-i-h-x-y-x*-j*-k*-x*-h*-i*-x*-j*-k*-x* CTGTAGC-TT-CGGCGAT-CTGATAC-TT-TT-AA-TGACCAA-ACCACCT-AA-GTATCAG-ATCGCCG-AA- (SEQ ID NO: 51) TGACCAA-ACCACCT-AA A4a: CTGTAGCTTCGGCGATCTGATACTTTTAATGACCAAACCACCTAAGTATCAG (SEQ ID NO: 52) A4b: /5Phos/ATCGCCGAATGACCAAACCACCTAA (SEQ ID NO: 53) A5: h-x-k-j-x-y-x*-l*-m*-x*-j*-k*-x* CTGATAC-TT-AGGTGGT-TTGGTCA-TT-TT-AA-CTCCACT-CCTACTC-AA-TGACCAA-ACCACCT-AA (SEQ ID NO: 54) A5a: CTGATACTTAGGTGGT (SEQ ID NO: 55) a5b: /5Phos/TTGGTCATTTTAACTCCACTCCTACTCAATGACCAAACCACCTAA (SEQ ID NO: 56) B2: x*-f*-g*-x*-d*-e*-x*-f*-g*-x*-y-x-e-d-x-c AA-GCTACAG-GACTACG-AA-TGCAATG-TCACGGT-AA-GCTACAG-GACTACG-AA-TT-TT-ACCGTGA- (SEQ ID NO: 57) CATTGCA-TT-ATCTATC B2a: AAGCTACAGGACTACGAATGCAATG (SEQ ID NO: 58) B2b: /5Phos/TCACGGTAAGCTACAGGACTACGAATTTTACCGTGACATTGCATTATCTATC (SEQ ID NO: 59) B3: x*-h*-i*-x*-f*-g*-x*-h*-i*-x*-y-x-g-f-x-e AA-GTATCAG-ATCGCCG-AA-GCTACAG-GACTACG-AA-GTATCAG-ATCGCCG-AA-TT-TT-CGTAGTC- (SEQ ID NO: 60) CTGTAGC-TT-ACCGTGA B3a: AAGTATCAGATCGCCGAAGCTACAG (SEQ ID NO: 61) B3b: /5Phos/GACTACGAAGTATCAGATCGCCGAATTTTCGTAGTCCTGTAGCTTACCGTGA (SEQ ID NO: 62) B4: x_j_k*-x*-h*-i*-x*-j*-k*-x*-y-x-i-h-x-g AA-TGACCAA-ACCACCT-AA-CTCCACT-CCTACTC-AA-TT-TT-AGGTGGT-TTGGTCA-TT-CGGCGAT (SEQ ID NO: 63) B5a: AATGACCAAACCACCTAACTCCACTCCTACTCAATTTTAGGTGGT (SEQ ID NO: 64) B5b: /5Phos/TTGGTCATTCGGCGAT (SEQ ID NO: 65) I: x*-b*-c*-x*-a* AA-TGGCAGA-GATAGAT-AA-GAGTTTG (SEQ ID NO: 66)

Fuel for the walker system. The sequences are listed below as text sequences annotated with segment names.

A: z-x-b-c-y-x*-a*-d*-y*-c*-b*-x* AAGTAGT-GATTGAGCG-TGATGAA-TG-TC-ACTACTT-CAACTCG-CA-TTCATCA-CGCTCAA-TC (SEQ ID NO: 67) Aa: AAGTAGTGATTGAGCGTGATGAATGTCACTACTTCAACTCGCATTCATC (SEQ ID NO: 68) Ab: /5Phos/ACGCTCAATC (SEQ ID NO: 69) B: c-y-d-a-x-y*-c*-b*-x*-a*-d*-y* TGATGAA-TG-CGAGTTG-AAGTAGT-GA-CA-TTCATCA-CGCTCAA-TC-ACTACTT-CAACTCG-CA (SEQ ID NO: 70) Ba: TGATGAATCCGAGTTGAAGTAGTGACATTCATCACGCTCAATCACTACT (SEQ ID NO: 71) Bb: /5Phos/TCAACTCGCA (SEQ ID NO: 72) I: x-y*-c*-b*-x*-a* GA-CA-TTCATCA-CGCTCAA-TC-ACTACTT (SEQ ID NO: 73) I-FAM: GACATTCATCACGCTCAATCACTACTT/36FAM (SEQ ID NO: 74)

Walker system. Sequence B is the same as described above for fuel for the walker system. W1 s is used as a splint strand for ligating strands W1 a and W1 b to produce W1; W2 s is used as a splint strand for ligating strands W2 a and W2 b to produce W2.

S1: GGTAGTTCTAGGCAGCTGAAGTAGTGATTGAGCGTGATGAATGTCACTACTTCAACTCGCATTCATCACGCTCAA (SEQ ID NO: 75) TC S1a: GGTAGTTCTAGGCAGCTGAAGTAGTGATTGAGCGT (SEQ ID NO: 76) S1b: /5Phos/GATGAATGTCACTACTTCAACTCGCATTCATCACGCTCAATC (SEQ ID NO: 77) S2: TCATAGGCACCGTCAGACAGGATAGAGCAGTGCATAGATAGTCATAGCCTTGGACCTGCCTAGAACTACC (SEQ ID NO: 78) S3: GTCCAAGGCTATGACTATCTATGCACT (SEQ ID NO: 79) S4: GCTCTATCCTGTCTGCTGAAGTAGTGATTGAGCGTGATGAATGTCACTACTTCAACTCGCATTCATCACGCTCAA (SEQ ID NO: 80) TC S4a: GCTCTATCCTGTCTGCTGAAGTAGTGATTGAGCGT (SEQ ID NO: 81) S4b: /5Phos/GATGAATGTCACTACTTCAACTCGCATTCATCACGCTCAATC (SEQ ID NO: 82) S5: ACGGTGCCTATGACATGGTACTCAGCT (SEQ ID NO: 83) S6: GCTCGTATCTGGTCGCTGAAGTAGTGATTGAGCGTGATGAATGTCACTACTTCAACTCGCATTCATCACGCTCAA (SEQ ID NO: 84) TC S6a: GCTCGTATCTGGTCGCTGAAGTAGTGATTGAGCGT (SEQ ID NO: 85) 26b: /5Phos/GATGAATGTCACTACTTCAACTCGCATTCATCACGCTCAATC (SEQ ID NO: 86) S7: CGTAAGTCGCAGAGTATGCCATTGCCTCATCAGCGTAGCATCGAGATCTAAGTTAGTAACTCTGGCAGCCTGGTA (SEQ ID NO: 87) GAGCGAGCCTATCGTCCTGATGTACGACCAGATACGAGCAGCTGAGTACCATG S7truncated: CGTAAGTCGCAGAGTATGCCATTGCCTCATCAGCGTAGCATCGAGATCTAAGTTAGTAACTCTGGCAGCCTGGTA (SEQ ID NO: 88) GAGCGAGCCTATCGTCCTGATGTACGACCAGATACGAGC S8-TMR: /5TMRN/TACATCAGGACGATAGGCTCGCTCTAC (SEQ ID NO: 89) S8-JOE: /5JOEN/TACATCAGGACGATAGGCTCGCTCTAC (SEQ ID NO: 90) S9: CAGGCTGCCAGAGTTCTGAAGTAGTGATTGAGCGTGATGAATGTCATACTTCAACTCGCATTCATCACGCTCAAT (SEQ ID NO: 91) C S9a: CAGGCTGCCAGAGTTCTGAAGTAGTGATTGAGCGT (SEQ ID NO: 92) S9b: /5Phos/GATGAATGTCACTACTTCAACTCGCATTCATCACGCTCAATC (SEQ ID NO: 93) S10-TMR: /5TMRN/ACTAACTTAGATCTCGATGCTACGCTG (SEQ ID NO: 94) S10-JOE: /5JOEN/ACTAACTTAGATCTCGATGCTACGCTG (SEQ ID NO: 95) S11: ATGAGGCAATGGCATTAGAAGTAGTGATTGAGCGTGATGAATGTCACTACTTCAACTCGCATTCATCACGCTCAA (SEQ ID NO: 96) TC S11a: ATGAGGCAATGGCATTAGAAGTAGTGATTGAGCGT (SEQ ID NO: 97) S11b: /5Phos/GATGAATGTCACTACTTCAACTCGCATTCATCACGCTCAATC (SEQ ID NO: 98) S12-FAM: /56FAM/ACTCTGCGACTTACG (SEQ ID NO: 99) W1: TTGCCTCGTATCCTAACCGAACGGACTCCAGGACATTCATCACGCTCAATCACTACTT (SEQ ID NO: 100) W1a: TTGCCTCGTATCCTAACCGAACGGACTCC (SEQ ID NO: 101) W1b: AGGACATTCATCACGCTCAATCACTACTT/BHQ-1/ (SEQ ID NO: 102) W1s: CGTGATGAATGTCCTGGAGTCCGTTCGGTT (SEQ ID NO: 103) W2: GTCCGTTCGGTTAGGATACGAGGCAATCCAGGACATTCATCACGCTCAATCACTACTT (SEQ ID NO: 104) W2a: GTCCGTTCGGTTAGGATACGAGGCAATCC (SEQ ID NO: 105) W2b: AGGACATTCATCACGCTCAATCACTACTT/BHQ-1/ (SEQ ID NO: 106) W2s: CGTGATGAATGTCCTGGATTGCCTCGTATC (SEQ ID NO: 107)

Example 18 Detecting the Subcellular Localization and Abundance of a Target mRNAs Using a Geometric Fluorescent Barcode

Two collections of hairpin monomers are generated. The first collection of hairpin monomers comprises nine unique nucleic acids which co-exist metastably in the absence of a target mRNA and autonomously self-assemble into a tetrahedron upon detection of an mRNA encoding GAP-43. The first hairpin monomer comprises an initiator binding domain which is complementary to a fragment of an mRNA encoding GAP-43 and is labeled with FITC, the third hairpin monomer is labeled with rhodamine and the fifth hairpin monomer is labeled with Lucifer Yellow.

The second collection of hairpin monomers comprises nine unique nucleic acids which co-exist metastably in the absence of a target mRNA and autonomously self-assemble into a tetrahedron upon detection of an mRNA encoding β-tubulin. The first hairpin monomer comprises an initiator binding domain which is complementary to a fragment of an mRNA encoding β-tubulin and is labeled with FITC, the second hairpin monomer is labeled with rhodamine and the third hairpin monomer is labeled with Lucifer Yellow.

Hippocampal neurons are transfected with the two collections of hairpin monomers and the cells are cultured for a period of time. The transfected hippocampal neurons are then imaged using high resolution fluorescence microscopy. Unique geometric fluorescent barcodes formed by the first collection of hairpin monomers is observed in the hippocampal nerve cell bodies where a tetrahedron comprising the nine nucleic acids of the first collection of hair pin monomers is bound to the mRNA encoding GAP-43. In addition, unique geometric fluorescent barcodes formed by the second collection of hairpin monomers is observed in the dendrites and axons of the hippocampal neurons where a tetrahedron comprising the nine nucleic acids of the second collection of hair pin monomers is bound to the mRNA encoding β-tubulin.

Example 19 Detecting a Target mRNA in a Using a Geometric Fluorescent Barcode

A collection of hairpin monomers is generated. The collection of hairpin monomers comprises nine unique nucleic acids which co-exist metastably in the absence of a target mRNA and autonomously self-assemble into a tetrahedron upon detection of a target mRNA. The first hairpin monomer comprises an initiator binding domain which is complementary to a fragment of a target mRNA. The fourth hairpin monomer comprises a toehold which catalyzes the release of the target RNA upon formation of the tetrahedron. The first hairpin monomer is labeled with FITC and a quencher, the fourth hairpin monomer is labeled with Cascade Blue and a quencher, and the sixth hairpin monomer is labeled with TRITC and a quencher. The quencher quenches the fluorescence of the fluorophore label in the hairpin conformation, but not when the nucleic acids are assembled as a tetrahedron.

Fibroblast cells are electroporated to transfer the collection of hairpin monomers into the cells. The fibroblast cells are cultured for a period of time. The electroporated fibroblast cells are then imaged using high resolution fluorescence microscopy and the fluorescence of the fluorophores assembled in geometric barcodes is observed. The formation of the tetrahedron catalyzes the release of the target mRNA from the initiator binding domain of the first hairpin monomer and the target mRNA is free to catalyze the formation of multiple geometric fluorescent barcodes, which results in an amplification of the signal.

Example 20 Detecting a Low Abundance Target mRNA in a using a Geometric Fluorescent Barcode

A collection of hairpin monomers is generated. The collection of hairpin monomers comprises nine unique nucleic acids that co-exist metastably in the absence of a target mRNA and autonomously self-assemble into a tetrahedron upon detection of a target mRNA. The first hairpin monomer comprises an initiator binding domain which is complementary to a fragment of a target mRNA which is present in fibroblast cells in low abundance. The fourth hairpin monomer comprises a toehold which catalyzes the release of the target RNA upon formation of the tetrahedron. The first, fourth, fifth and sixth hairpin monomers are labeled with FITC and a quencher, which quenches the fluorescence of the of the FITC label in the hairpin conformation, but not when the nucleic acids are assembled as a tetrahedron.

Fibroblast cells are electroporated to transfer the collection of hairpin monomers into the cells. The fibroblast cells are cultured for a period of time. The electroporated fibroblast cells are then imaged using traditional fluorescence microscopy and the fluorescence of FITC assembled in geometric barcodes is observed. Since the formation of the tetrahedron catalyzes the release of the target mRNA from the initiator binding domain of the first hairpin monomer, the target mRNA is free to catalyze the formation of multiple geometric fluorescent barcodes, which results in an amplification of the signal.

Example 21 Detecting a Target mRNA by Aggregating Dispersed Green Fluorescent Protein

A transgenic mouse which expresses mRNA encoding a GFP fusion protein under the control of the human ubiquitin C (UBC) promoter is obtained. The GFP fusion protein comprises green fluorescent protein fused to a peptide adaptor. Tail tip fibroblast cells are harvested from the transgenic mouse and are grown in culture.

A collection of hairpin monomers is generated. The collection of hairpin monomers comprises nucleic acids which co-exist metastably in the absence of a target mRNA and autonomously self-assemble based on nucleated dendritic growth into a binary tree upon detection of a target mRNA. The first hairpin monomer comprises an initiator binding domain which is complementary to a fragment of the target mRNA. The hairpin monomers further comprise an aptamer which binds the peptide adaptor with nanomolar affinity.

The transgenic fibroblast cells are electroporated to transfer the collection of hairpin monomers into the cells. The fibroblast cells are cultured for a period of time. The electroporated fibroblast cells are then imaged using traditional fluorescence microscopy. Bright foci of aggregated GFP are observed in the electroporated cells.

Example 22 Detecting a Target mRNA by Aggregating Dispersed Green Fluorescent Protein

A collection of hairpin monomers is generated. The collection of hairpin monomers comprises at least three unique nucleic acids which co-exist metastably in the absence of a target mRNA and autonomously self-assemble based on a catalytic branch formation system into a trimer upon detection of a target mRNA. The first hairpin monomer comprises an aptamer which binds to a first peptide adaptor with micromolar affinity and an initiator binding domain which is complementary to a fragment of the target mRNA. Formation of the trimer catalyzes the release of the target mRNA from the initiator binding domain. The second hairpin monomer comprises an aptamer which binds to a second peptide adaptor with micromolar affinity and the third hairpin monomer comprises an aptamer which binds to a third peptide adaptor with micromolar affinity.

Fibroblast cells are infected with a retroviral vector comprising genes encoding GFP fused to a first peptide adaptor, RFP fused to a second peptide adaptor, and YFP fused to a third peptide adaptor. The fibroblast cells are cultured and background levels of GFP, RFP and YFP fluorescence are observed to confirm expression of the proteins. The fibroblast cells are then transfected with the first, second and third hairpin monomers. The fibroblast cells are cultured for a period of time. The electroporated fibroblast cells are then imaged using fluorescence correlation spectroscopy and nucleotide trimers comprising GFP, RFP and YFP fluorescent signals are observed.

Example 23 Detecting a Target mRNA by Fluorescence Resonance Energy Transfer

A collection of hairpin monomers is generated. The collection of hairpin monomers comprises four unique nucleic acids which co-exist metastably in the absence of a target mRNA and autonomously self-assemble based on a catalytic 4-arm junction formation system upon detection of a target mRNA. The first hairpin monomer comprises an aptamer on both the 5′ and 3′ ends which binds to a first peptide adaptor and an initiator binding domain which is complementary to a fragment of the target mRNA. Formation of the 4-arm junction catalyzes the release of the target mRNA from the initiator binding domain. The second and fourth hairpin monomers comprise an aptamer on both the 5′ and 3′ ends which binds to a second peptide adaptor and the third hairpin monomer comprises an aptamer on both the 5′ and 3′ ends which binds to the first peptide adaptor.

HELA cells are infected with a retroviral vector comprising genes encoding GFP fused to a first peptide adaptor and BFP fused to a second peptide adaptor. The HELA cells are cultured and background levels of GFP and BFP fluorescence are observed to confirm expression of the proteins. The GFP and BFP expressing cells are then infected with a retroviral vector comprising genes encoding the first, second, third and fourth hairpin monomers. The cells are imaged using fluorescent microscopy techniques to detect formation of the 4-arm junction by FRET.

Example 24 Detecting a Target mRNA using a Geometric Barcode to Organize Fluorescent Proteins

A collection of hairpin monomers is generated. The collection of hairpin monomers comprises six unique nucleic acids which co-exist metastably in the absence of a target mRNA and autonomously self-assemble based on a catalytic tetrahedron formation system upon detection of a target mRNA. Formation of the tetrahedron catalyzes the release of the target mRNA from the initiator binding domain. The first hairpin monomer comprises an initiator binding domain which is complementary to a fragment of a target mRNA and an aptamer which binds to a first peptide adaptor. The second hairpin monomer comprises an aptamer which binds to a second peptide adaptor, the third hairpin monomer comprises an aptamer which binds to a third peptide adaptor, and the fourth hairpin monomer comprises an aptamer which binds to a first peptide adaptor.

Fibroblast cells are infected with a adenoviral vector comprising genes encoding GFP fused to a first peptide adaptor, RFP fused to a second peptide adaptor, and YFP fused to a third peptide adaptor. The fibroblast cells are cultured and levels of GFP, RFP and YFP fluorescence are observed to confirm expression of the proteins.

The fibroblast cells are electroporated to transfer the collection of hairpin monomers into the cells. The fibroblast cells are cultured for a period of time. The electroporated fibroblast cells are then imaged using high resolution fluorescence microscopy. Observation of an ordered assembly of the fluorescent proteins in a geometric barcode indicates that the target gene is expressed. Since the formation of the tetrahedron catalyzes the release of the target mRNA from the initiator binding domain of the first hairpin monomer, the target mRNA is free to catalyze the formation of multiple fluorescent protein organizing structures.

Example 25 Detection of a Geometric Marker for Electron Cryomicroscopy

A transgenic mouse which expresses mRNAs encoding an initiator aptamer and a heat shock protein 60 (HSP60) fusion protein under the control of an inducible promoter is obtained. The HSP60 fusion protein comprises HSP60 fused to a peptide adaptor. Tail tip fibroblast cells are harvested from the transgenic mouse and are grown in culture.

A collection of hairpin monomers is generated. The collection of hairpin monomers comprises six unique nucleic acids which co-exist metastably in the absence of an initiator aptamer and autonomously self-assemble into a tetrahedron upon binding of a first hairpin monomer to the initiator aptamer.

The fibroblast cells are induced to express the HSP60 fusion protein transgene and the initiator aptamer. The cells are then transfected with the six unique nucleic acids. After a period of incubation the cells are lysed and the cytoplasm is imaged with electron cryomicroscopy. An electron dense geometric marker is observed to tag HSP60 proteins.

Example 26 Detection of a Geometric Marker for Electron Cryomicroscopy

A transgenic mouse which expresses mRNAs encoding a heat shock protein 60 (HSP60) fusion protein under the control of an inducible promoter is obtained. The HSP60 fusion protein comprises HSP60 fused to a peptide adaptor. Tail tip fibroblast cells are harvested from the transgenic mouse and are grown in culture.

A collection of hairpin monomers and a switchable nucleic acid aptamer is generated. The collection of hairpin monomers comprises twenty unique nucleic acids which co-exist metastably when unbound to the aptamer and autonomously self-assemble into a tetrahedron upon binding of a first hairpin monomer to the initiator aptamer. The switchable nucleic acid aptamer is triggered to an active open conformation upon binding to the HSP60 fusion protein.

The fibroblast cells are induced to express the HSP60 fusion protein transgene and then transfected with the six unique nucleic acids and the switchable nucleic acid aptamer. After a period of incubation the cells are flash frozen and fractured. The fractured cells are imaged with electron cryomicroscopy. An electron dense geometric marker is observed to tag HSP60 proteins.

Example 27 Catalytic Formation of a DNA Tetrahedron

FIG. 43 a-d depict the reaction schematic for the catalytic formation of a tetrahedron. In the absence of initiator T, hairpins A1, A2, A3, B1, B2, B3, C1, C2, and C3 are metastable. In the presence of initiator T, the hairpins are catalyzed by T to form a tetrahedron.

Initiator T first catalyze A1, A2, and A3 to form a three-arm junction, resulting in the opening of hairpins A1, A2, and A3. Open hairpin A1 interacts with and opens hairpin B1, which then opens hairpin C1. In a similar fashion, open hairpin A2 causes hairpin B2 to open, which then opens hairpin C2; and open hairpin A3 causes hairpin B3 to open, which then opens hairpin C3. Finally, open hairpin C1 hybridizes with opened hairpin B2; open hairpin C2 hybridizes with opened hairpin B3; and open hairpin C3 hybridizes with open hairpin B1—completing the catalytic formation of the tetrahedrons.

The foregoing description and Examples detail certain specific embodiments of the invention and describes the best mode contemplated by the inventors. It will be appreciated, however, that no matter how detailed the foregoing may appear in text, the invention may be practiced in many ways and the invention should be construed in accordance with the appended claims and any equivalents thereof.

While the present teachings have been described in terms of these exemplary embodiments, the skilled artisan will readily understand that numerous variations and modifications of these exemplary embodiments are possible without undue experimentation. All such variations and modifications are within the scope of the current teachings. The foregoing examples are provided to better illustrate the disclosed teachings and are not intended to limit the scope of the teachings presented herein.

All references cited herein, including patents, patent applications, papers, text books, and the like, and the references cited therein, to the extent that they are not already, are hereby incorporated by reference in their entirety. In the event that one or more of the incorporated literature and similar materials differs from or contradicts this application, including but not limited to defined terms, term usage, described techniques, or the like, this application controls.

FIGS. 1-36 are also described in U.S. patent application Ser. No. 12/152,893, which is herein incorporated by reference in its entirety. U.S. patent application Ser. No. 12/152,893 is also incorporated, without limitation, for the purposes of FIGS. 1-36. 

1. An imaging probe comprising: a collection of hairpin monomers comprising a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the collection of hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule, wherein the prescribed shape is imageable.
 2. The imaging probe of claim 1, wherein the collection of hairpin monomers comprises a first nucleic acid, a second nucleic acid, and a third nucleic acid.
 3. The imaging probe of claim 2, wherein the first, second and third nucleic acids each comprise a sequence to allow each to form a hairpin monomer.
 4. The imaging probe of claim 3, further comprising a detectable marker.
 5. The imaging probe of claim 3, wherein the detectable marker comprises GFP.
 6. The imaging probe of claim 3, wherein the first nucleic acid is labeled with a first fluorophore, the second nucleic acid is labeled with a second fluorophore, and the third nucleic acid is labeled with a third fluorophore.
 7. The imaging probe of claim 6, wherein the prescribed shape comprises a rigid asymmetric 3-dimensional structure that arranges the first, second, and third fluorophores in a pattern that is distinguishable from fluorescence attributable to fluorophores not incorporated in the 3-dimensional structure.
 8. The imaging probe of claim 1, further comprising: at least one fluorescent protein.
 9. The imaging probe of claim 8, wherein the fluorescent protein is covalently attached to at least one of the first, second, or third nucleic acids.
 10. The imaging probe of claim 9, wherein the fluorescent protein is fused to at least one peptide tag, and wherein the peptide tag binds to at least one of the first, second and/or third nucleic acids.
 11. The imaging probe of claim 1, wherein the collection of hairpin monomers self-assemble into a binary tree.
 12. The imaging probe of claim 1 further comprising: a first fluorescent protein fused to a first peptide tag; a second fluorescent protein fused to a second peptide tag; and a third fluorescent protein fused to a third peptide tag; wherein the first peptide tag binds to the first hairpin monomer; the second peptide binds to the second hairpin monomer; and the third peptide tag binds to the third hairpin monomer.
 13. The imaging probe of claim 12 wherein the hairpin monomers self-assemble into a trimer comprising the first hairpin monomer, the second hairpin monomer and the third hairpin monomer; and wherein the first hairpin monomer is bound to the first peptide tag fused to the first fluorescent protein, the second hairpin monomer is bound to the second peptide tag fused to the second fluorescent protein, and the third hairpin monomer is bound to the third peptide tag fused to the third fluorescent protein.
 14. The imaging probe of claim 13 wherein the first, second and third hairpin monomers self-assemble into a rigid asymmetric 3-dimensional structure comprising: the first hairpin monomer bound to the first peptide tag fused to the first fluorescent protein, the second hairpin monomer bound to the second peptide tag fused to the second fluorescent protein and the third hairpin monomer bound to the third peptide tag fused to the third fluorescent protein; wherein the asymmetric 3-dimensional structure arranges the first, second, and third fluorescent proteins in a pattern that is distinguishable from fluorescence attributable to fluorescent proteins not incorporated in the 3-dimensional structure.
 15. The imaging probe of claim 1 wherein the first hairpin monomer comprises an aptamer which binds to a target peptide with specific sub-nanomolar binding affinity.
 16. The imaging probe of claim 15 the first hairpin monomer is triggered into an activated, open conformation upon binding to the target protein.
 17. The imaging probe of claim 15 wherein the prescribed shape comprises a 3-dimensional structure that is detectable by electron cryomicroscopy (ECT).
 18. The imaging probe of claim 17, wherein the 3-dimensional structure is asymmetric.
 19. The imaging probe of claim 1, comprising 3 to one million hairpin monomers.
 20. The imaging probe of claim 1, comprising 3 to 50 hairpin monomers.
 21. The imaging probe of claim 1, wherein an order of binding between the first hairpin monomer, the second hairpin monomer and the third hairpin monomer determines the prescribed shape.
 22. The imaging probe of claim 1, wherein the first hairpin monomer comprises a first fluorescent marker and the second hairpin monomer comprises a second fluorescent marker, and wherein a change from individual hairpin monomers to the prescribed shape results in a structural rearrangement that results in a change in FRET characteristics of at least one fluorescent maker.
 23. A protein organizer comprising: a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the first, second, and third hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule, wherein the first hairpin monomer is linked to a first protein, and wherein the second hairpin monomer is linked to a second protein.
 24. The protein organizer of claim 23, wherein the protein comprises a fluorescent protein.
 25. The protein organizer of claim 24, wherein the first hairpin monomer, the second hairpin monomer, a third hairpin monomer, and a fourth hairpin monomer self-assemble into a four-arm-junction in the presence of the target nucleotide, such that the first fluorescent protein and the second fluorescent protein are co-localized on an end of a duplex arm of the four-arm-junction.
 26. A method for labeling a target with a geometric barcode, comprising: providing a collection of hairpin monomers comprising at least a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the first hairpin monomer is labeled with a first fluorophore, the second hairpin monomer is labeled with a second fluorophore, and the third hairpin monomer is labeled with a third fluorophore, and wherein the collection of hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule.
 27. A method for conjugating fluorescent protein with a target molecule, comprising: providing a fluorescent protein linked to a peptide adaptor, providing a first hairpin monomer, a second hairpin monomer, and a third hairpin monomer, wherein the first, second, and third hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule, wherein the first hairpin monomer comprises an aptamer, and wherein the aptamer binds to the fluorescent protein linked peptide adaptor; and combining the fluorescent protein linked to a peptide adaptor and the first hairpin monomer, the second hairpin monomer, and the third hairpin monomer, with a target molecule.
 28. A method for FRET based target detection, comprising: providing a first hairpin monomer that is linked to a first fluorescent protein; providing a second hairpin monomer that is linked to a first fluorescent protein; providing a third hairpin monomer that is linked to a second fluorescent protein; providing a fourth hairpin monomer that is linked to a second fluorescent protein, wherein the first, second, third and fourth hairpin monomers autonomously self-assemble into a four-arm-junction in the presence of a target, such that the first fluorescent protein and the second fluorescent protein are co-localized on an end of a duplex arm of the four-arm-junction, thereby altering a FRET signal of the fluorescent proteins.
 29. A method for detecting a target molecule with a geometric structural marker, comprising: applying a collection of hairpin monomers comprising a first hairpin monomer and a second hairpin monomer to a sample, wherein the collection of hairpin monomers autonomously self-assemble into a prescribed shape upon detection of a target molecule, wherein the prescribed shape is electron dense; detecting the prescribed shape; and using the detected shape as an indicator of the target molecule.
 30. The method of claim 29, further comprising sufficient hairpin monomers to self-assemble into a tetrahedron.
 31. The method of claim 30, wherein nine hairpin monomers are employed to form the tetrahedron. 